The multirate multi-input systems have different updating periods and sampling periods such that the conventional identification algorithms cannot be used to identify such multirate systems. By using the auxiliary mod...The multirate multi-input systems have different updating periods and sampling periods such that the conventional identification algorithms cannot be used to identify such multirate systems. By using the auxiliary model identification idea, the multiinnovation stochastic gradient algorithm is developed to estimate the parameters of multirate systems. Finally, an illustrative example is given to verify the effectiveness of the proposed algorithm.展开更多
Wavelet transform was introduced to detect and eliminate outliers in time-frequency domain. The outlier rejection and multirate information extraction were initially incorporated by wavelet transform, a new outlier re...Wavelet transform was introduced to detect and eliminate outliers in time-frequency domain. The outlier rejection and multirate information extraction were initially incorporated by wavelet transform, a new outlier rejecting multirate model for state estimation was proposed. The model is applied to state estimation with interacting multiple model, as the outlier is eliminated and more reasonable multirate information is extracted, the estimation accuracy is greatly enhanced. The simulation results prove that the new model is robust to outliers and the estimation performance is significantly improved.展开更多
In this article, floating quantization effects on multirate sampled-data control systems are studied. It shows that the solutions of multirate digital feedback control systems with nonlinear plant and with floating qu...In this article, floating quantization effects on multirate sampled-data control systems are studied. It shows that the solutions of multirate digital feedback control systems with nonlinear plant and with floating quantization in the controller are uniformly ultimately bounded if the associated linear systems consisting of linearization of the plant and controller with no quantization are Schur stable. Moreover, it also shows that the difference between the response of multirate digital controllers without quantizers and the same plant with floating quantization in the controllers can be made as small as desired by selecting proper quantization level.展开更多
Based on the multi-model principle, the fuzzy identification for nonlinear systems with multirate sampled data is studied.Firstly, the nonlinear system with multirate sampled data can be shown as the nonlinear weighte...Based on the multi-model principle, the fuzzy identification for nonlinear systems with multirate sampled data is studied.Firstly, the nonlinear system with multirate sampled data can be shown as the nonlinear weighted combination of some linear models at multiple local working points. On this basis, the fuzzy model of the multirate sampled nonlinear system is built. The premise structure of the fuzzy model is confirmed by using fuzzy competitive learning, and the conclusion parameters of the fuzzy model are estimated by the random gradient descent algorithm. The convergence of the proposed identification algorithm is given by using the martingale theorem and lemmas. The fuzzy model of the PH neutralization process of acid-base titration for hair quality detection is constructed to demonstrate the effectiveness of the proposed method.展开更多
The goal of this paper is to design a model-free optimal controller for the multirate system based on reinforcement learning.Sampled-data control systems are widely used in the industrial production process and multir...The goal of this paper is to design a model-free optimal controller for the multirate system based on reinforcement learning.Sampled-data control systems are widely used in the industrial production process and multirate sampling has attracted much attention in the study of the sampled-data control theory.In this paper,we assume the sampling periods for state variables are different from periods for system inputs.Under this condition,we can obtain an equivalent discrete-time system using the lifting technique.Then,we provide an algorithm to solve the linear quadratic regulator(LQR)control problem of multirate systems with the utilization of matrix substitutions.Based on a reinforcement learning method,we use online policy iteration and off-policy algorithms to optimize the controller for multirate systems.By using the least squares method,we convert the off-policy algorithm into a model-free reinforcement learning algorithm,which only requires the input and output data of the system.Finally,we use an example to illustrate the applicability and efficiency of the model-free algorithm above mentioned.展开更多
Two kinds of wavelet-based elements have been constructed to analyze the stability of plates and shells and the static displacement of 3D elastic problems.The scaling functions of B-spline wavelet on the interval（BSW...Two kinds of wavelet-based elements have been constructed to analyze the stability of plates and shells and the static displacement of 3D elastic problems.The scaling functions of B-spline wavelet on the interval（BSWI） are employed as interpolating functions to construct plate and shell elements for stability analysis and 3D elastic elements for static mechanics analysis.The main advantages of BSWI scaling functions are the accuracy of B-spline functions approximation and various wavelet-based elements for structural analysis.The performances of the present elements are demonstrated by typical numerical examples.展开更多
This paper presents a mathematical model that analyzes the throughput of the IEEE 802.11b distributed coordination function （DCF） with the collision aware rate adaptation （CARA） algorithm. IEEE 802.11 WLANs provid...This paper presents a mathematical model that analyzes the throughput of the IEEE 802.11b distributed coordination function （DCF） with the collision aware rate adaptation （CARA） algorithm. IEEE 802.11 WLANs provide multiple transmission rates to improve system throughput by adapting the transmission rate to the current channel conditions. The system throughput is determined by some stations using low transmission rates due to bad channel conditions. CARA algorithm does not disturb the existing IEEE 802.11b formats and it can be easily incorporated into the commercial wireless local area networks （WLAN） devices. Finally, we verify our findings with simulation.展开更多
In this paper, a rate adaptive protocol AMARF (Adaptive Multirate Auto Rate Fallback) for multirate IEEE 802.11 networks is proposed. In AMARF, each data rate is assigned a unique success threshold, which is a criteri...In this paper, a rate adaptive protocol AMARF (Adaptive Multirate Auto Rate Fallback) for multirate IEEE 802.11 networks is proposed. In AMARF, each data rate is assigned a unique success threshold, which is a criterion to judge when to switch a rate to the next higher one, and the success thresholds can be adjusted dynamically in an adaptive manner according to the running conditions, such as packet length and channel parameters. Moreover, the proposed protocol can be implemented by software without any change to the current IEEE 802.11 standards. Simulation result shows that AMARF yields significantly higher throughput than other existing schemes including ARF and its variants, in various running conditions.展开更多
This paper focuses on the fast rate fault detection filter (FDF) problem for a class of multirate sampled-data (MSD) systems. A lifting technique is used to convert such an MSD system into a linear time-invariant disc...This paper focuses on the fast rate fault detection filter (FDF) problem for a class of multirate sampled-data (MSD) systems. A lifting technique is used to convert such an MSD system into a linear time-invariant discrete-time one and an unknown input observer (UIO) is considered as FDF to generate residual. The design of FDF is formulated as an H∞ optimization problem and a solvable condition as well as an optimal solution are derived. The causality of the residual generator can be guaranteed so that the fast rate residual can be implemented via inverse lifting. A numerical example is included to demonstrate the feasibility of the obtained results.展开更多
Edge detection is a fundamental issue in image analysis. This paper proposes multirate algorithms for efficient implementation of edge detector, and a design example is illustrated.The multirate (decimation and/or int...Edge detection is a fundamental issue in image analysis. This paper proposes multirate algorithms for efficient implementation of edge detector, and a design example is illustrated.The multirate (decimation and/or interpolation) signal processing algorithms can achieve considerable savings in computation and storage. The proposed algorithms result in mapping relations of their z-transfer functions between non-multirate and multirate mathematical expressions in terms of time-varying coefficient instead of traditional polyphase decomposition counterparts.The mapping properties can be readily utilized to efficiently analyze and synthesize multirate edge detection filters. The Very high-speed Hardware Description Language (VHDL) simulation results verify efficiency of the algorithms for real-time Field Programmable Gate-Array (FPGA)implementation.展开更多
The basic analysis and synthesis approaches for multirate sampled-data control system are reviewed. After giving the definition and some properties of multirate system are given, its origination, development and desig...The basic analysis and synthesis approaches for multirate sampled-data control system are reviewed. After giving the definition and some properties of multirate system are given, its origination, development and design methods are discussed in detail. Finally, some remarks, expectations and conclusions on the present research status and the research directions are given.展开更多
Multirate systems are abundant in industry; for example, many soft-sensor design problems are related to modeling, parameter identification, or state estimation involving multirate systems. The study of multirate syst...Multirate systems are abundant in industry; for example, many soft-sensor design problems are related to modeling, parameter identification, or state estimation involving multirate systems. The study of multirate systems goes back to the early 1950's, and has become an active research area in systems and control. This paper briefly surveys the history of development in the area of multirate systems, and introduces some basic concepts and latest results on multirate systems, including a polynomial transformation technique and the lifting technique as tools for handling multirate systems, lifted state space models, parameter identification of dual-rate systems, how to determine fast single-rate models from dual-rate models and directly from dual-rate data, and a hierarchical identification method for general multirate systems. Finally, some further research topics for multirate systems are given.展开更多
Previous analyses of fractal modulation were carried out mostly from a signle perspective or a subband, but the analyses from the perspective of multiscale synthesis have not been found yet; while multiscale synthesis...Previous analyses of fractal modulation were carried out mostly from a signle perspective or a subband, but the analyses from the perspective of multiscale synthesis have not been found yet; while multiscale synthesis is just the essence of the mutlirate diversity which is the most important characteristic of fractal modulation. As for the mutlirate diversity of fractal modulation, previous studies only dealt with the general outspread of its concept, lacked the thorough and intensive quantitative comparison and analysis. In light of the above fact, from the perspective of multiscale synthesis, in this paper we provide a comprehensive analysis of the multirate diversity of fractal modulation and corresponding quantitative analysis. The results show that mutlirate diversity, which is a fusion of frequency diversity and time diversity, pays an acceptable price in spectral efficiency in exchange for a significant improvement in bit error rate. It makes fractal modulation particularly suitable for the channels whose bandwidth and duration parameters axe unknown or cannot be predicted to the transmitter. Surely it is clearly of great significance for reliable communications. Moreover, we also attain the ability to flexibly make various rate-bandwidth tradeoffs between the transmitter and the receiver, to freely select the reception time and to expediently control the total bandwidth. Furthermore, the acquisitions or improvements of these fine features could provide support of the technical feasibility for the electromagnetic spectrum control technology in a complex electromagnetic environment.展开更多
Emerging wireless community cloud enables usergenerated video content to be shared and consumed in a social context. However, the nature of shared wireless medium and timevarying channels seriously limits the quality ...Emerging wireless community cloud enables usergenerated video content to be shared and consumed in a social context. However, the nature of shared wireless medium and timevarying channels seriously limits the quality of service(QoS), partially owing to the lack of mechanisms for effectively utilizing multi-rate channel resources. In this paper, the joint optimization of admission control and rate adaptation is proposed, resulting in a bandwidth-aware rate-adaptive admission control(BRAC) scheme to provide bandwidth guarantee for sharing social multimedia contents. The analytical approach leads to the following major contributions:(1) a bandwidth-aware rate selection(BRS) algorithm to optimally meet the bandwidth requirement of the data session and channel conditions at the physical layer;(2) a routing-coupled rate adaption and admission control algorithm to admit data sessions with bandwidth guarantee. Moreover, extensive numerical simulations suggest that BRAC is efficient and effective in meeting the bandwidth requirements for sharing social multimedia contents. These insights will shed light on communication system implementation for multimedia content sharing over multirate wireless community cloud.展开更多
In this paper,a multirate processing approach for microwave imaging is presented.This approach has the advantages of largely compressing the raw spectral data for imaging,greatly reducing the storage requirement and e...In this paper,a multirate processing approach for microwave imaging is presented.This approach has the advantages of largely compressing the raw spectral data for imaging,greatly reducing the storage requirement and enhancing the processing efficiency.To demonstrateits applicability,the proposed approach is tested on both simulated and experimental data.展开更多
In this paper, we investigate the self-encoded multirate and the multimedia (SEMM) transmission. In SEMM system, the spreading codes are derived from its own previously transmitted bits rather than the pseudorandom co...In this paper, we investigate the self-encoded multirate and the multimedia (SEMM) transmission. In SEMM system, the spreading codes are derived from its own previously transmitted bits rather than the pseudorandom code generator. We employ block chip interleaving at the transmitter to combat the deep fading over the channels. At the receiver, decorrelation scheme separates the combined signals not only to reduce the crosstalk between different applications, but also provide a better estimation for the despreading sequence. Interference cancelation (IC) is also adopted to improve both the correlation detection and iterative detection (ID) performance. The simulation results show that the proposed scheme significantly improves performance over fading channels.展开更多
Multirate digital control system is a periodically time-variant (PTV) system in its essence. It bas many' super capability', such as obtaining arbitrarily-large gain- margin, simultaneous stabilization, strong...Multirate digital control system is a periodically time-variant (PTV) system in its essence. It bas many' super capability', such as obtaining arbitrarily-large gain- margin, simultaneous stabilization, strong stabilization, decentralized control, etc. Utilizing freedom aroused from the multirate sampling of system output, this paper assigns poles of the closedloop system robustly, and so improves the resistance of the system to perturbation.展开更多
Based on the sampler decomposition method and modified Z transform, this paper proposes a pulse transfer function matrix description of the multivariable multirate sampling systems. This multirate sampling system mode...Based on the sampler decomposition method and modified Z transform, this paper proposes a pulse transfer function matrix description of the multivariable multirate sampling systems. This multirate sampling system model has a simple structure, and can be used as a basis for the analysis and synthesis of the multirate sampling systems.展开更多
Based on the suitably defined multivariable version of Kranc operators and the extended input and output vectors, the multirate sampling plant is transformed to a equivalent time invariant single rate one, then the t...Based on the suitably defined multivariable version of Kranc operators and the extended input and output vectors, the multirate sampling plant is transformed to a equivalent time invariant single rate one, then the transfer function model of the multivariable multirate sampling plant is obtained. By combining this plant model with the time invariant description of the multirate controller in terms of extended vectors, the closed loop transfer function model of the multirate feedback control system can be determinated. This transfer function model has a very simple structure, and can be used as a basis for the analysis and synthesis of the multirate sampling feedback control systems in the frequency domain.展开更多
基金supported by the National Natural Science Foundation of China (60973043)
文摘The multirate multi-input systems have different updating periods and sampling periods such that the conventional identification algorithms cannot be used to identify such multirate systems. By using the auxiliary model identification idea, the multiinnovation stochastic gradient algorithm is developed to estimate the parameters of multirate systems. Finally, an illustrative example is given to verify the effectiveness of the proposed algorithm.
文摘Wavelet transform was introduced to detect and eliminate outliers in time-frequency domain. The outlier rejection and multirate information extraction were initially incorporated by wavelet transform, a new outlier rejecting multirate model for state estimation was proposed. The model is applied to state estimation with interacting multiple model, as the outlier is eliminated and more reasonable multirate information is extracted, the estimation accuracy is greatly enhanced. The simulation results prove that the new model is robust to outliers and the estimation performance is significantly improved.
基金Supported by National Natural Science Foundation of China(10671069) the program of Shanghai Priority Academic Discipline
文摘In this article, floating quantization effects on multirate sampled-data control systems are studied. It shows that the solutions of multirate digital feedback control systems with nonlinear plant and with floating quantization in the controller are uniformly ultimately bounded if the associated linear systems consisting of linearization of the plant and controller with no quantization are Schur stable. Moreover, it also shows that the difference between the response of multirate digital controllers without quantizers and the same plant with floating quantization in the controllers can be made as small as desired by selecting proper quantization level.
基金supported by the National Natural Science Foundation of China(61863034)。
文摘Based on the multi-model principle, the fuzzy identification for nonlinear systems with multirate sampled data is studied.Firstly, the nonlinear system with multirate sampled data can be shown as the nonlinear weighted combination of some linear models at multiple local working points. On this basis, the fuzzy model of the multirate sampled nonlinear system is built. The premise structure of the fuzzy model is confirmed by using fuzzy competitive learning, and the conclusion parameters of the fuzzy model are estimated by the random gradient descent algorithm. The convergence of the proposed identification algorithm is given by using the martingale theorem and lemmas. The fuzzy model of the PH neutralization process of acid-base titration for hair quality detection is constructed to demonstrate the effectiveness of the proposed method.
基金This work was supported by National Key R&D Program of China(No.2018YFB1308404).
文摘The goal of this paper is to design a model-free optimal controller for the multirate system based on reinforcement learning.Sampled-data control systems are widely used in the industrial production process and multirate sampling has attracted much attention in the study of the sampled-data control theory.In this paper,we assume the sampling periods for state variables are different from periods for system inputs.Under this condition,we can obtain an equivalent discrete-time system using the lifting technique.Then,we provide an algorithm to solve the linear quadratic regulator(LQR)control problem of multirate systems with the utilization of matrix substitutions.Based on a reinforcement learning method,we use online policy iteration and off-policy algorithms to optimize the controller for multirate systems.By using the least squares method,we convert the off-policy algorithm into a model-free reinforcement learning algorithm,which only requires the input and output data of the system.Finally,we use an example to illustrate the applicability and efficiency of the model-free algorithm above mentioned.
基金supported by the National Natural Science Foundation of China (No. 50805028)the Key Project of Chinese Ministry of Education (No. 210170)+1 种基金Guangxi key Technologies R & D Program of China (Nos. 1099022-1 and 0900705 003)supported in part by the Excellent Talents in Guangxi Higher Education Institutions of China
文摘Two kinds of wavelet-based elements have been constructed to analyze the stability of plates and shells and the static displacement of 3D elastic problems.The scaling functions of B-spline wavelet on the interval（BSWI） are employed as interpolating functions to construct plate and shell elements for stability analysis and 3D elastic elements for static mechanics analysis.The main advantages of BSWI scaling functions are the accuracy of B-spline functions approximation and various wavelet-based elements for structural analysis.The performances of the present elements are demonstrated by typical numerical examples.
文摘This paper presents a mathematical model that analyzes the throughput of the IEEE 802.11b distributed coordination function （DCF） with the collision aware rate adaptation （CARA） algorithm. IEEE 802.11 WLANs provide multiple transmission rates to improve system throughput by adapting the transmission rate to the current channel conditions. The system throughput is determined by some stations using low transmission rates due to bad channel conditions. CARA algorithm does not disturb the existing IEEE 802.11b formats and it can be easily incorporated into the commercial wireless local area networks （WLAN） devices. Finally, we verify our findings with simulation.
文摘In this paper, a rate adaptive protocol AMARF (Adaptive Multirate Auto Rate Fallback) for multirate IEEE 802.11 networks is proposed. In AMARF, each data rate is assigned a unique success threshold, which is a criterion to judge when to switch a rate to the next higher one, and the success thresholds can be adjusted dynamically in an adaptive manner according to the running conditions, such as packet length and channel parameters. Moreover, the proposed protocol can be implemented by software without any change to the current IEEE 802.11 standards. Simulation result shows that AMARF yields significantly higher throughput than other existing schemes including ARF and its variants, in various running conditions.
基金Supported by National Natural Science Foundation of P. R. China (60374021)the Natural Science Foundation of Shandong Province (Y2002G05)the Youth Scientists Foundation of Shandong Province (03BS091, 05BS01007) and Education Ministry Foundation of P. R. China (20050422036)
文摘This paper focuses on the fast rate fault detection filter (FDF) problem for a class of multirate sampled-data (MSD) systems. A lifting technique is used to convert such an MSD system into a linear time-invariant discrete-time one and an unknown input observer (UIO) is considered as FDF to generate residual. The design of FDF is formulated as an H∞ optimization problem and a solvable condition as well as an optimal solution are derived. The causality of the residual generator can be guaranteed so that the fast rate residual can be implemented via inverse lifting. A numerical example is included to demonstrate the feasibility of the obtained results.
文摘Edge detection is a fundamental issue in image analysis. This paper proposes multirate algorithms for efficient implementation of edge detector, and a design example is illustrated.The multirate (decimation and/or interpolation) signal processing algorithms can achieve considerable savings in computation and storage. The proposed algorithms result in mapping relations of their z-transfer functions between non-multirate and multirate mathematical expressions in terms of time-varying coefficient instead of traditional polyphase decomposition counterparts.The mapping properties can be readily utilized to efficiently analyze and synthesize multirate edge detection filters. The Very high-speed Hardware Description Language (VHDL) simulation results verify efficiency of the algorithms for real-time Field Programmable Gate-Array (FPGA)implementation.
文摘The basic analysis and synthesis approaches for multirate sampled-data control system are reviewed. After giving the definition and some properties of multirate system are given, its origination, development and design methods are discussed in detail. Finally, some remarks, expectations and conclusions on the present research status and the research directions are given.
基金Supported by the Natural Sciences and Engineering Research Council of Canada and National Natural Science Foundation of P.R.China
文摘Multirate systems are abundant in industry; for example, many soft-sensor design problems are related to modeling, parameter identification, or state estimation involving multirate systems. The study of multirate systems goes back to the early 1950's, and has become an active research area in systems and control. This paper briefly surveys the history of development in the area of multirate systems, and introduces some basic concepts and latest results on multirate systems, including a polynomial transformation technique and the lifting technique as tools for handling multirate systems, lifted state space models, parameter identification of dual-rate systems, how to determine fast single-rate models from dual-rate models and directly from dual-rate data, and a hierarchical identification method for general multirate systems. Finally, some further research topics for multirate systems are given.
基金supported by the National Natural Science Foundation of China (Grant No. 10731050)the Program for Changjiang Scholars and Innovative Research Team in University of the Ministry of Education of China (Grant No. IRTO0742)
文摘Previous analyses of fractal modulation were carried out mostly from a signle perspective or a subband, but the analyses from the perspective of multiscale synthesis have not been found yet; while multiscale synthesis is just the essence of the mutlirate diversity which is the most important characteristic of fractal modulation. As for the mutlirate diversity of fractal modulation, previous studies only dealt with the general outspread of its concept, lacked the thorough and intensive quantitative comparison and analysis. In light of the above fact, from the perspective of multiscale synthesis, in this paper we provide a comprehensive analysis of the multirate diversity of fractal modulation and corresponding quantitative analysis. The results show that mutlirate diversity, which is a fusion of frequency diversity and time diversity, pays an acceptable price in spectral efficiency in exchange for a significant improvement in bit error rate. It makes fractal modulation particularly suitable for the channels whose bandwidth and duration parameters axe unknown or cannot be predicted to the transmitter. Surely it is clearly of great significance for reliable communications. Moreover, we also attain the ability to flexibly make various rate-bandwidth tradeoffs between the transmitter and the receiver, to freely select the reception time and to expediently control the total bandwidth. Furthermore, the acquisitions or improvements of these fine features could provide support of the technical feasibility for the electromagnetic spectrum control technology in a complex electromagnetic environment.
基金sponsored by the following funds:the National Natural Science Foundation of China(No.61502381)the Fundamental Research Funds for the Central Universities(No.xjj2015065)the China Post Doctoral Science Foundation(No.2015M570836)
文摘Emerging wireless community cloud enables usergenerated video content to be shared and consumed in a social context. However, the nature of shared wireless medium and timevarying channels seriously limits the quality of service(QoS), partially owing to the lack of mechanisms for effectively utilizing multi-rate channel resources. In this paper, the joint optimization of admission control and rate adaptation is proposed, resulting in a bandwidth-aware rate-adaptive admission control(BRAC) scheme to provide bandwidth guarantee for sharing social multimedia contents. The analytical approach leads to the following major contributions:(1) a bandwidth-aware rate selection(BRS) algorithm to optimally meet the bandwidth requirement of the data session and channel conditions at the physical layer;(2) a routing-coupled rate adaption and admission control algorithm to admit data sessions with bandwidth guarantee. Moreover, extensive numerical simulations suggest that BRAC is efficient and effective in meeting the bandwidth requirements for sharing social multimedia contents. These insights will shed light on communication system implementation for multimedia content sharing over multirate wireless community cloud.
文摘In this paper,a multirate processing approach for microwave imaging is presented.This approach has the advantages of largely compressing the raw spectral data for imaging,greatly reducing the storage requirement and enhancing the processing efficiency.To demonstrateits applicability,the proposed approach is tested on both simulated and experimental data.
文摘In this paper, we investigate the self-encoded multirate and the multimedia (SEMM) transmission. In SEMM system, the spreading codes are derived from its own previously transmitted bits rather than the pseudorandom code generator. We employ block chip interleaving at the transmitter to combat the deep fading over the channels. At the receiver, decorrelation scheme separates the combined signals not only to reduce the crosstalk between different applications, but also provide a better estimation for the despreading sequence. Interference cancelation (IC) is also adopted to improve both the correlation detection and iterative detection (ID) performance. The simulation results show that the proposed scheme significantly improves performance over fading channels.
基金Supported by the National Natural Science Foundation of China(No. 69774024 )
文摘Multirate digital control system is a periodically time-variant (PTV) system in its essence. It bas many' super capability', such as obtaining arbitrarily-large gain- margin, simultaneous stabilization, strong stabilization, decentralized control, etc. Utilizing freedom aroused from the multirate sampling of system output, this paper assigns poles of the closedloop system robustly, and so improves the resistance of the system to perturbation.
文摘Based on the sampler decomposition method and modified Z transform, this paper proposes a pulse transfer function matrix description of the multivariable multirate sampling systems. This multirate sampling system model has a simple structure, and can be used as a basis for the analysis and synthesis of the multirate sampling systems.
文摘Based on the suitably defined multivariable version of Kranc operators and the extended input and output vectors, the multirate sampling plant is transformed to a equivalent time invariant single rate one, then the transfer function model of the multivariable multirate sampling plant is obtained. By combining this plant model with the time invariant description of the multirate controller in terms of extended vectors, the closed loop transfer function model of the multirate feedback control system can be determinated. This transfer function model has a very simple structure, and can be used as a basis for the analysis and synthesis of the multirate sampling feedback control systems in the frequency domain.
