This study presents a numerical method for determining the minimum time required for the states of one class of integro-differential equations of the first kind to reach its attainable region by assuming the forcing t...This study presents a numerical method for determining the minimum time required for the states of one class of integro-differential equations of the first kind to reach its attainable region by assuming the forcing terms of the equations as controls. These equations consist of integro-differential parts containing weakly singular kernels. The feasibility of the numerical method is demonstrated by comparing the minimum time and corresponding possible time by using extreme controls to reach the attainable region under different initial conditions.展开更多
This article studies the consensus problem with directed graphs for general linear multi-agent systems.New distributed state-feedback protocols with dynamic event-triggered(DET)mechanisms are proposed for directed gra...This article studies the consensus problem with directed graphs for general linear multi-agent systems.New distributed state-feedback protocols with dynamic event-triggered(DET)mechanisms are proposed for directed graphs that are strongly connected and weight-balanced,general strongly connected,and have spanning trees,respectively.It is proven that strictly positive minimum inter-event times(MIETs)are ensured using the designed DET mechanisms.Several numerical examples are presented to illustrate the effectiveness of the theoretical results.Compared with existing results,our results have the following merits:1)DET mechanisms are designed to determine the sampling instants,which can reduce the communication frequency between agents compared with static mechanisms;2)We focus on the consensus problem on directed graphs,which is more general than existing related results on undirected graphs;3)The existence of positive MIETs is shown to be guaranteed by the designed DET sampling strategies while existing related results can only exclude Zeno behavior.展开更多
This paper investigates the consensus control of multi-agent systems(MASs) with constrained input using the dynamic event-triggered mechanism(ETM).Consider the MASs with small-scale networks where a centralized dynami...This paper investigates the consensus control of multi-agent systems(MASs) with constrained input using the dynamic event-triggered mechanism(ETM).Consider the MASs with small-scale networks where a centralized dynamic ETM with global information of the MASs is first designed.Then,a distributed dynamic ETM which only uses local information is developed for the MASs with large-scale networks.It is shown that the semi-global consensus of the MASs can be achieved by the designed bounded control protocol where the Zeno phenomenon is eliminated by a designable minimum inter-event time.In addition,it is easier to find a trade-off between the convergence rate and the minimum inter-event time by an adjustable parameter.Furthermore,the results are extended to regional consensus of the MASs with the bounded control protocol.Numerical simulations show the effectiveness of the proposed approach.展开更多
This paper will investigate global exponential stability analysis for a class of switched positive nonlinear systems under minimum dwell time switching, whose nonlinear functions for each subsystem are constrained in ...This paper will investigate global exponential stability analysis for a class of switched positive nonlinear systems under minimum dwell time switching, whose nonlinear functions for each subsystem are constrained in a sector field by two odd symmetric piecewise linear functions and whose system matrices for each subsystem are Metzler. A class of multiple time-varying Lyapunov functions is constructed to obtain the computable sufficient conditions on the stability of such switched nonlinear systems within the framework of minimum dwell time switching.All present conditions can be solved by linear/nonlinear programming techniques. An example is provided to demonstrate the effectiveness of the proposed result.展开更多
The wireline formation tester （WFT） is an important tool for formation evaluation, such as calculating the formation pressure and permeability, identifying the fluid type, and determining the interface between oil a...The wireline formation tester （WFT） is an important tool for formation evaluation, such as calculating the formation pressure and permeability, identifying the fluid type, and determining the interface between oil and water. However, in a low porosity and low permeability formation, the supercharge pressure effect exists, since the mudcake has a poor sealing ability. The mudcake cannot isolate the hydrostatic pressure of the formation around the borehole and the mud seeps into the formations, leading to inaccurate formation pressure measurement. At the same time, the tool can be easily stuck in the low porosity/low permeability formation due to the long waiting and testing time. We present a method for determining the minimum testing time for the wireline formation tester. The pressure distribution of the mudcake and the formation were respectively calculated with the finite element method （FEM）. The radius of the influence of mud pressure was also computed, and the minimum testing time in low porosity/low permeability formations was determined within a range of values for different formation permeabilities. The determination of the minimum testing time ensures an accurate formation pressure measurement and minimizes possible accidents due to long waiting and testing time.展开更多
The previous Decentralised Cognitive Medium Access Control(DC-MAC) protocol allows Secondary Users(SUs) to independently search for spectrum access opportunities without the need for a central coordinator.DC-MAC assum...The previous Decentralised Cognitive Medium Access Control(DC-MAC) protocol allows Secondary Users(SUs) to independently search for spectrum access opportunities without the need for a central coordinator.DC-MAC assumes that the detection scheme is ideal at the Physical(PHY) layer.In fact,a more complex detection algorithm is impractical in distributed spectrum sharing scenarios.Energy Detection(ED) at the PHY layer has become the most common method because of its low computational and implementation complexities.Thus,it is essential to integrate the DC-MAC with ED at the PHY layer.However,ED requires the Minimum Sampling Time(MST)duration to achieve the target detection probability in low Signal-to-Noise Ratio(SNR)environments.Otherwise,it cannot achieve the expected detection performance.In this paper,we derive an accurate expression of MST for ED in low SNR environments.Then,we propose an Optimised DC-MAC(ODC-MAC) protocol which is based on MST,and which amends the aforementioned problems of DC-MAC with ED.Moreover,the closed-form expressions for the unreliable data transmission probability are derived for both DC-MAC and ODC-MAC.We show that the simulation results agree well with the theoretical analyses.The proposed ODC-MAC can improve the data transmission reliability and enhance the throughput compared to the performance of the traditional DC-MAC.展开更多
By using a phase-plane analysis method,the minimum-time trajectory plan-ning problem of a manipulator moving along a given geometric path subject to the con-straints of joint velocities and accelerations is solved in ...By using a phase-plane analysis method,the minimum-time trajectory plan-ning problem of a manipulator moving along a given geometric path subject to the con-straints of joint velocities and accelerations is solved in this paper.The simulation resultfor the first three joints of PUMA-560 is given.展开更多
The relation of matter wave, which is well-known as a hypothesis proposed by de Broglie in 1923, gave basis for establishing the quantum mechanics. After that, experimental results revealed that a micro particle has a...The relation of matter wave, which is well-known as a hypothesis proposed by de Broglie in 1923, gave basis for establishing the quantum mechanics. After that, experimental results revealed that a micro particle has a wave nature. However, the theoretical validity of the relation itself has never been revealed since his proposal. Theoretical basis that a micro particle has a wave nature has been thus disregarded in the unsolved state. The diffusion equation having been accepted as Fick’s second law was derived from the theory of Markov process in mathematics. It was then revealed that the diffusivity D depends on an angular momentum of a micro particle in a local space. The fact being unable to discriminate between micro particles in a local space resulted in having to accept the existence of minimum time t<sub>0 </sub>(>0) in the quantum mechanics. Based on t<sub>0</sub> and D obtained here, the theoretical validity of relation of matter wave was confirmed. Denying the density theorem in mathematics for time in physics indicates that the probabilistic interpretation is essentially indispensable for understanding the quantum mechanics. The logical necessity of quantum theory itself is thus understandable through introducing t<sub>0</sub> into the Newton mechanics. It is remarkable that the value of t<sub>0</sub> between 1.14×10<sup>-17</sup> s ≤ t<sub>0 </sub>≤1.76×10<sup>-14 </sup>s obtained here is extremely larger than that of the well-known Planck time t<sub>p</sub>=5.396×10<sup>-44 </sup>s.展开更多
The traditional tangent impulse interception problem does not consider the influence of actual deviation.However,by taking the actual state deviation of the interceptor into the orbit design process,an interception or...The traditional tangent impulse interception problem does not consider the influence of actual deviation.However,by taking the actual state deviation of the interceptor into the orbit design process,an interception orbit that is more robust than the nominal orbit can be obtained.Therefore,we study the minimum time interception problem and the minimum terminal interception error problem under tangent impulse conditions and give an orbit optimization method that considers the interception time and the interception uncertainty.First,we express the interceptor's transfer time equation as a form of flight path angle,establish a global optimization model for solving the minimum time tangent impulse interception and give a hybrid optimization algorithm based on Augmented Lagrange Genetic Algorithm-Sequential Quadratic Programming(ALGA-SQP).Secondly,we use the universal time equation and Bootstrap resampling technology to calculate the interceptor's terminal error distribution and establish the relevant global optimization model by using the circumscribed cuboid volume of the interceptor's terminal position error ellipsoid as the optimization index.Finally,we combined the above two singleobjective optimization models to establish a global multi-objective optimization model that considers interception time and interception uncertainty and gave a hybrid multi-objective optimization algorithm based on Non-dominated Sorting Genetic Algorithm Ⅱ-Goal Achievement Method(NSGA2-GAM).The simulation example verifies the effectiveness of this method.展开更多
Under dense urban fading environment, performance of joint multi-path parameter estimation method based on traditional point signal model degrades seriously. In this paper, a new space and time signal model based on m...Under dense urban fading environment, performance of joint multi-path parameter estimation method based on traditional point signal model degrades seriously. In this paper, a new space and time signal model based on multipath distribution function is given after new space and time manifold is reconstructed. Then joint spacetime signal subspace is obtained by converting acquired channel from time domain to frequency domain .Then space and time spectrum is formulated by the space sub-matrix and time sub-matrix taken out of joint space-time signal subspace, and parameters are estimated by searching the minimum eigenvalues of the space matrix and the time matrix. Lastly, A space and time parameters matching process is performed by using the orthogonal property between joint noise subspace and the space-time manifold. In contrast with tradition MUSIC, the algorithm we present here only need two 1- dimension searching and was not sensitive to different distribution function.展开更多
Switching Markov jump linear system(SMJLS),a special hybrid system,has attracted a lot of studies recently.SMJLS is governed by stochastic and deterministic commutations.This paper focuses on the switching strategy wh...Switching Markov jump linear system(SMJLS),a special hybrid system,has attracted a lot of studies recently.SMJLS is governed by stochastic and deterministic commutations.This paper focuses on the switching strategy which stabilizes the SMJLS in a finite time interval in order to further expand the existing results and investigate new aspects of such systems.Several sufficient conditions for finite-time stability of discrete-time SMJLS are provided,and the numerical problems in these sufficient conditions are solved by solving linear matrix inequalities(LMIs).Finally,numerical examples are given to show the feasibility and effectiveness of the results.展开更多
Characterization of a mobile radio channel plays an important role in designing a reliable wireless communication system. Such channels are analyzed by two state model, namely satisfactory and outage state. This paper...Characterization of a mobile radio channel plays an important role in designing a reliable wireless communication system. Such channels are analyzed by two state model, namely satisfactory and outage state. This paper presents the analysis to estimate fading parameters of wireless channel with omission of certain outage durations which are considered as “Tolerance time”. Minimum outage duration which can be tolerated by a wireless fading channel to achieve desired packet error rate is defined as tolerance time. Normally a system with tolerable minimum outage time is analyzed based on Fade Duration Distribution (FDD) function over Rayleigh channel. In this paper Weibull function is used as FDD for varying tolerance time. The approach is simple and in general applicable from Rayleigh to Nakagami channels. The analysis is extended to study the effect of Tolerance time on channel fading statistics such as Average Fade Duration (AFD) and frequency of outage. Further the effects of various fade margin and Doppler spread on fading parameters are also investigated. The analysis can also be used in case of timeout expiration, connection resetting and congestion window control.展开更多
The blockage probability and the blockage time are two important indexes for assessing the blockage efficiency of cluster munitions against the runway. The improved region-by-region searching method and the random sam...The blockage probability and the blockage time are two important indexes for assessing the blockage efficiency of cluster munitions against the runway. The improved region-by-region searching method and the random sampling method are proposed to calculate the blockage time by considering the minimum number of craters which need to be repaired after attack. A minimum leave window (MLW) with the minimum number of craters is found out as a region to be repaired,the blockage probability and the blockage time are calculated by the two methods in which the impact points of the sub-munitions are generated with Monte-Carlo simulation technique. An example is given to show the reasonableness of the two methods under the conditions of adequacy simulating times and enough sampling times,and how to choose the methods in application.展开更多
Receding horizon H∞ control scheme which can deal with both the H∞ disturbance attenuation and mean square stability is proposed for a class of discrete-time Markovian jump linear systems when minimizing a given qua...Receding horizon H∞ control scheme which can deal with both the H∞ disturbance attenuation and mean square stability is proposed for a class of discrete-time Markovian jump linear systems when minimizing a given quadratic performance criteria. First, a control law is established for jump systems based on pontryagin’s minimum principle and it can be constructed through numerical solution of iterative equations. The aim of this control strategy is to obtain an optimal control which can minimize the cost function under the worst disturbance at every sampling time. Due to the difficulty of the assurance of stability, then the above mentioned approach is improved by determining terminal weighting matrix which satisfies cost monotonicity condition. The control move which is calculated by using this type of terminal weighting matrix as boundary condition naturally guarantees the mean square stability of the closed-loop system. A sufficient condition for the existence of the terminal weighting matrix is presented in linear matrix inequality （LMI） form which can be solved efficiently by available software toolbox. Finally, a numerical example is given to illustrate the feasibility and effectiveness of the proposed method.展开更多
文摘This study presents a numerical method for determining the minimum time required for the states of one class of integro-differential equations of the first kind to reach its attainable region by assuming the forcing terms of the equations as controls. These equations consist of integro-differential parts containing weakly singular kernels. The feasibility of the numerical method is demonstrated by comparing the minimum time and corresponding possible time by using extreme controls to reach the attainable region under different initial conditions.
基金supported in part by the Natural Science Foundation of China(62273227,92367203)the Open Research Project of the State Key Laboratory of Industrial Control Technology,China(ICT2024B68)。
文摘This article studies the consensus problem with directed graphs for general linear multi-agent systems.New distributed state-feedback protocols with dynamic event-triggered(DET)mechanisms are proposed for directed graphs that are strongly connected and weight-balanced,general strongly connected,and have spanning trees,respectively.It is proven that strictly positive minimum inter-event times(MIETs)are ensured using the designed DET mechanisms.Several numerical examples are presented to illustrate the effectiveness of the theoretical results.Compared with existing results,our results have the following merits:1)DET mechanisms are designed to determine the sampling instants,which can reduce the communication frequency between agents compared with static mechanisms;2)We focus on the consensus problem on directed graphs,which is more general than existing related results on undirected graphs;3)The existence of positive MIETs is shown to be guaranteed by the designed DET sampling strategies while existing related results can only exclude Zeno behavior.
基金supported in part by the National Natural Science Foundation of China(51939001,61976033,62273072)the Natural Science Foundation of Sichuan Province (2022NSFSC0903)。
文摘This paper investigates the consensus control of multi-agent systems(MASs) with constrained input using the dynamic event-triggered mechanism(ETM).Consider the MASs with small-scale networks where a centralized dynamic ETM with global information of the MASs is first designed.Then,a distributed dynamic ETM which only uses local information is developed for the MASs with large-scale networks.It is shown that the semi-global consensus of the MASs can be achieved by the designed bounded control protocol where the Zeno phenomenon is eliminated by a designable minimum inter-event time.In addition,it is easier to find a trade-off between the convergence rate and the minimum inter-event time by an adjustable parameter.Furthermore,the results are extended to regional consensus of the MASs with the bounded control protocol.Numerical simulations show the effectiveness of the proposed approach.
基金supported by the National Natural Science Foundation of China(61673198)the Provincial Natural Science Foundation of Liaoning Province(20180550473)
文摘This paper will investigate global exponential stability analysis for a class of switched positive nonlinear systems under minimum dwell time switching, whose nonlinear functions for each subsystem are constrained in a sector field by two odd symmetric piecewise linear functions and whose system matrices for each subsystem are Metzler. A class of multiple time-varying Lyapunov functions is constructed to obtain the computable sufficient conditions on the stability of such switched nonlinear systems within the framework of minimum dwell time switching.All present conditions can be solved by linear/nonlinear programming techniques. An example is provided to demonstrate the effectiveness of the proposed result.
文摘The wireline formation tester （WFT） is an important tool for formation evaluation, such as calculating the formation pressure and permeability, identifying the fluid type, and determining the interface between oil and water. However, in a low porosity and low permeability formation, the supercharge pressure effect exists, since the mudcake has a poor sealing ability. The mudcake cannot isolate the hydrostatic pressure of the formation around the borehole and the mud seeps into the formations, leading to inaccurate formation pressure measurement. At the same time, the tool can be easily stuck in the low porosity/low permeability formation due to the long waiting and testing time. We present a method for determining the minimum testing time for the wireline formation tester. The pressure distribution of the mudcake and the formation were respectively calculated with the finite element method （FEM）. The radius of the influence of mud pressure was also computed, and the minimum testing time in low porosity/low permeability formations was determined within a range of values for different formation permeabilities. The determination of the minimum testing time ensures an accurate formation pressure measurement and minimizes possible accidents due to long waiting and testing time.
基金supported by the National Natural Science Foundation of China under Grants No.61271259,No.61301123the Chongqing Natural Science Foundation under Grant No.CTSC2011jjA40006+2 种基金the Research Project of Chongqing Education Commission under Grants No.KJ120501,No.KJ120502,No.KJ130536the Special Fund of Chongqing Key Laboratory(CSTC)the Project of Chongqing Municipal Education Commission under Grant No.Kjzh11206
文摘The previous Decentralised Cognitive Medium Access Control(DC-MAC) protocol allows Secondary Users(SUs) to independently search for spectrum access opportunities without the need for a central coordinator.DC-MAC assumes that the detection scheme is ideal at the Physical(PHY) layer.In fact,a more complex detection algorithm is impractical in distributed spectrum sharing scenarios.Energy Detection(ED) at the PHY layer has become the most common method because of its low computational and implementation complexities.Thus,it is essential to integrate the DC-MAC with ED at the PHY layer.However,ED requires the Minimum Sampling Time(MST)duration to achieve the target detection probability in low Signal-to-Noise Ratio(SNR)environments.Otherwise,it cannot achieve the expected detection performance.In this paper,we derive an accurate expression of MST for ED in low SNR environments.Then,we propose an Optimised DC-MAC(ODC-MAC) protocol which is based on MST,and which amends the aforementioned problems of DC-MAC with ED.Moreover,the closed-form expressions for the unreliable data transmission probability are derived for both DC-MAC and ODC-MAC.We show that the simulation results agree well with the theoretical analyses.The proposed ODC-MAC can improve the data transmission reliability and enhance the throughput compared to the performance of the traditional DC-MAC.
文摘By using a phase-plane analysis method,the minimum-time trajectory plan-ning problem of a manipulator moving along a given geometric path subject to the con-straints of joint velocities and accelerations is solved in this paper.The simulation resultfor the first three joints of PUMA-560 is given.
文摘The relation of matter wave, which is well-known as a hypothesis proposed by de Broglie in 1923, gave basis for establishing the quantum mechanics. After that, experimental results revealed that a micro particle has a wave nature. However, the theoretical validity of the relation itself has never been revealed since his proposal. Theoretical basis that a micro particle has a wave nature has been thus disregarded in the unsolved state. The diffusion equation having been accepted as Fick’s second law was derived from the theory of Markov process in mathematics. It was then revealed that the diffusivity D depends on an angular momentum of a micro particle in a local space. The fact being unable to discriminate between micro particles in a local space resulted in having to accept the existence of minimum time t<sub>0 </sub>(>0) in the quantum mechanics. Based on t<sub>0</sub> and D obtained here, the theoretical validity of relation of matter wave was confirmed. Denying the density theorem in mathematics for time in physics indicates that the probabilistic interpretation is essentially indispensable for understanding the quantum mechanics. The logical necessity of quantum theory itself is thus understandable through introducing t<sub>0</sub> into the Newton mechanics. It is remarkable that the value of t<sub>0</sub> between 1.14×10<sup>-17</sup> s ≤ t<sub>0 </sub>≤1.76×10<sup>-14 </sup>s obtained here is extremely larger than that of the well-known Planck time t<sub>p</sub>=5.396×10<sup>-44 </sup>s.
文摘The traditional tangent impulse interception problem does not consider the influence of actual deviation.However,by taking the actual state deviation of the interceptor into the orbit design process,an interception orbit that is more robust than the nominal orbit can be obtained.Therefore,we study the minimum time interception problem and the minimum terminal interception error problem under tangent impulse conditions and give an orbit optimization method that considers the interception time and the interception uncertainty.First,we express the interceptor's transfer time equation as a form of flight path angle,establish a global optimization model for solving the minimum time tangent impulse interception and give a hybrid optimization algorithm based on Augmented Lagrange Genetic Algorithm-Sequential Quadratic Programming(ALGA-SQP).Secondly,we use the universal time equation and Bootstrap resampling technology to calculate the interceptor's terminal error distribution and establish the relevant global optimization model by using the circumscribed cuboid volume of the interceptor's terminal position error ellipsoid as the optimization index.Finally,we combined the above two singleobjective optimization models to establish a global multi-objective optimization model that considers interception time and interception uncertainty and gave a hybrid multi-objective optimization algorithm based on Non-dominated Sorting Genetic Algorithm Ⅱ-Goal Achievement Method(NSGA2-GAM).The simulation example verifies the effectiveness of this method.
基金the National Natural Science Foundation of China (60372022).
文摘Under dense urban fading environment, performance of joint multi-path parameter estimation method based on traditional point signal model degrades seriously. In this paper, a new space and time signal model based on multipath distribution function is given after new space and time manifold is reconstructed. Then joint spacetime signal subspace is obtained by converting acquired channel from time domain to frequency domain .Then space and time spectrum is formulated by the space sub-matrix and time sub-matrix taken out of joint space-time signal subspace, and parameters are estimated by searching the minimum eigenvalues of the space matrix and the time matrix. Lastly, A space and time parameters matching process is performed by using the orthogonal property between joint noise subspace and the space-time manifold. In contrast with tradition MUSIC, the algorithm we present here only need two 1- dimension searching and was not sensitive to different distribution function.
基金the National Natural Science Foundation of China(No.61573237)the“111 Project”(No.D18003)the Program of China Scholarship Council(No.201906895021)。
文摘Switching Markov jump linear system(SMJLS),a special hybrid system,has attracted a lot of studies recently.SMJLS is governed by stochastic and deterministic commutations.This paper focuses on the switching strategy which stabilizes the SMJLS in a finite time interval in order to further expand the existing results and investigate new aspects of such systems.Several sufficient conditions for finite-time stability of discrete-time SMJLS are provided,and the numerical problems in these sufficient conditions are solved by solving linear matrix inequalities(LMIs).Finally,numerical examples are given to show the feasibility and effectiveness of the results.
文摘Characterization of a mobile radio channel plays an important role in designing a reliable wireless communication system. Such channels are analyzed by two state model, namely satisfactory and outage state. This paper presents the analysis to estimate fading parameters of wireless channel with omission of certain outage durations which are considered as “Tolerance time”. Minimum outage duration which can be tolerated by a wireless fading channel to achieve desired packet error rate is defined as tolerance time. Normally a system with tolerable minimum outage time is analyzed based on Fade Duration Distribution (FDD) function over Rayleigh channel. In this paper Weibull function is used as FDD for varying tolerance time. The approach is simple and in general applicable from Rayleigh to Nakagami channels. The analysis is extended to study the effect of Tolerance time on channel fading statistics such as Average Fade Duration (AFD) and frequency of outage. Further the effects of various fade margin and Doppler spread on fading parameters are also investigated. The analysis can also be used in case of timeout expiration, connection resetting and congestion window control.
基金Sponsored by the National Nature Science Foundation of China(60604020)Pre-research Project of National University of Defense Technology(JC2006-02-01)
文摘The blockage probability and the blockage time are two important indexes for assessing the blockage efficiency of cluster munitions against the runway. The improved region-by-region searching method and the random sampling method are proposed to calculate the blockage time by considering the minimum number of craters which need to be repaired after attack. A minimum leave window (MLW) with the minimum number of craters is found out as a region to be repaired,the blockage probability and the blockage time are calculated by the two methods in which the impact points of the sub-munitions are generated with Monte-Carlo simulation technique. An example is given to show the reasonableness of the two methods under the conditions of adequacy simulating times and enough sampling times,and how to choose the methods in application.
基金supported by the National Natural Science Foundation of China (60974001)Jiangsu "Six Personnel Peak" Talent-Funded Projects
文摘Receding horizon H∞ control scheme which can deal with both the H∞ disturbance attenuation and mean square stability is proposed for a class of discrete-time Markovian jump linear systems when minimizing a given quadratic performance criteria. First, a control law is established for jump systems based on pontryagin’s minimum principle and it can be constructed through numerical solution of iterative equations. The aim of this control strategy is to obtain an optimal control which can minimize the cost function under the worst disturbance at every sampling time. Due to the difficulty of the assurance of stability, then the above mentioned approach is improved by determining terminal weighting matrix which satisfies cost monotonicity condition. The control move which is calculated by using this type of terminal weighting matrix as boundary condition naturally guarantees the mean square stability of the closed-loop system. A sufficient condition for the existence of the terminal weighting matrix is presented in linear matrix inequality （LMI） form which can be solved efficiently by available software toolbox. Finally, a numerical example is given to illustrate the feasibility and effectiveness of the proposed method.
