This paper considers the design problem of static output feedback H ∞ controllers for descriptor linear systems with linear matrix inequality (LMI) approach. Necessary and sufficient conditions for the existence of...This paper considers the design problem of static output feedback H ∞ controllers for descriptor linear systems with linear matrix inequality (LMI) approach. Necessary and sufficient conditions for the existence of a static output feedback H ∞ controller are given in terms of LMIs. Furthermore, the design method of H ∞ controllers is provided using the solutions to the LMIs.展开更多
Aim To study the optimal guaranteed cost control problem via static output feedback for uncertain linear discrete time systems with norm bounded parameter uncertainty in both the state and the control input matric...Aim To study the optimal guaranteed cost control problem via static output feedback for uncertain linear discrete time systems with norm bounded parameter uncertainty in both the state and the control input matrices of the state space model. Methods\ An upper bound on a quadratic cost index was found for all admissible parameter uncertainties and minimized by using Lagrange multiplier approach. Results and Conclusion\ Sufficient conditions are given for the existence of a controller guaranteeing the closed loop system quadratic stability and providing an optimized bound. A numerical algorithm for solving the output feedback gain is also presented.展开更多
In this paper,the static output feedback stabilization for large-scale unstable second-order singular systems is investigated.First,the upper bound of all unstable eigenvalues of second-order singular systems is deriv...In this paper,the static output feedback stabilization for large-scale unstable second-order singular systems is investigated.First,the upper bound of all unstable eigenvalues of second-order singular systems is derived.Then,by using the argument principle,a computable stability criterion is proposed to check the stability of secondorder singular systems.Furthermore,by applying model reduction methods to original systems,a static output feedback design algorithm for stabilizing second-order singular systems is presented.A simulation example is provided to illustrate the effectiveness of the design algorithm.展开更多
Based on a kind of regular form, a Lyapunov matrix with special structure is presented to design the sliding surface matrix conveniently and then an effective algorithm is developed on it. A simple static output feedb...Based on a kind of regular form, a Lyapunov matrix with special structure is presented to design the sliding surface matrix conveniently and then an effective algorithm is developed on it. A simple static output feedback sliding mode control law without extra dynamic equation is given, such that the predefined sliding surface is reached in finite time for the general matching uncertainties. In the reported result, this extra dynamic equation is used for evaluating the norm bound of the unmeasured state vector. Finally, some examples are studied to illustrate the proposed approach.展开更多
This paper is concerned with the problem of designing robust H∞and H2static output feedback controllers for a class of discrete-time piecewise-affine singular systems with norm-bounded time-varying parameters uncerta...This paper is concerned with the problem of designing robust H∞and H2static output feedback controllers for a class of discrete-time piecewise-affine singular systems with norm-bounded time-varying parameters uncertainties. Based on a piecewise singular Lyapunov function combined with S-procedure,Projection lemma and some matrix inequality convexifying techniques,sufficient conditions in terms of linear matrix inequalities are given for the existence of an output-feedback controller for the discrete-time piecewiseaffine singular systems with a prescribed H∞disturbance attenuation level,and the H2norm is smaller than a given positive number. It is shown that the controller gains can be obtained by solving a family of LMIs parameterized by one or two scalar variables. The numerical examples are given to illustrate the effectiveness of the proposed design methods.展开更多
The design of H∞ reduced order controllers is known to be a non-convex optimization problem for which no generic solution exists. In this paper, the use of Particle Swarm Optimization （PSO） for the computation of H...The design of H∞ reduced order controllers is known to be a non-convex optimization problem for which no generic solution exists. In this paper, the use of Particle Swarm Optimization （PSO） for the computation of H~ static output feedbacks is investigated. Two approaches are tested. In a first part, a probabilistic-type PSO algorithm is defined for the computation of discrete sets of stabilizing static output feedback controllers. This method relies on a technique for random sample generation in a given domain. It is therefore used for computing a suboptimal Ha static output feedback solution, In a second part, the initial optimization problem is solved by PSO, the decision variables being the feedback gains. Results are compared with standard reduced order problem solvers using the COMPIeib （Constraint Matrix-optimization Problem Library） benchmark examples and appear to be much than satisfactory, proving the great potential of PSO techniques.展开更多
This study is concerned with the stabilization issue of nonlinear systems subject to parameter uncertainties. An interval type-2 T-S fuzzy model is used to represent the nonlinear systems subject to parameter uncertai...This study is concerned with the stabilization issue of nonlinear systems subject to parameter uncertainties. An interval type-2 T-S fuzzy model is used to represent the nonlinear systems subject to parameter uncertainties. An interval type-2 fuzzy static output feedback controller is designed to synthesize the interval type-2 T-S fuzzy systems. The membership-function-dependent stability conditions are derived by utilizing the information of upper and lower membership functions. The proposed stability conditions are presented in the form of linear matrix inequalities（LMIs）. LMI-based stability conditions for interval type-2 fuzzy static output feedback H_∞ control synthesis are also developed.Several simulation examples are given to show the superiority of the proposed approach.展开更多
This paper investigates the problem of robust exponential H∞ static output feedback controller design for a class of discrete-time switched linear systems with polytopic-type time-varying parametric uncertainties. Th...This paper investigates the problem of robust exponential H∞ static output feedback controller design for a class of discrete-time switched linear systems with polytopic-type time-varying parametric uncertainties. The objective is to design a switched static output feedback controller guaranteeing the exponential stability of the resulting closed-loop system with a minimized exponential H∞ performance under average dwell-time switching scheme. Based on a parameter-dependent discontinuous switched Lyapunov function combined with Finsler＇s lemma and Dualization lemma, some novel conditions for exponential H∞ performance analysis are first proposed and in turn the static output feedback controller designs are developed. It is shown that the controller gains can be obtained by solving a set of linear matrix inequalities （LMIs）, which are numerically efficient with commercially available software. Finally, a simulation example is provided to illustrate the effectiveness of the proposed approaches.展开更多
This paper is concerned with the problems of robust admissibility and static output feedback( SOF)stabilization for a class of discrete-time switched singular systems with norm-bounded parametric uncertainties.The obj...This paper is concerned with the problems of robust admissibility and static output feedback( SOF)stabilization for a class of discrete-time switched singular systems with norm-bounded parametric uncertainties.The objective is to design a suitable robust SOF controller guaranteeing the regularity,causality and asymptotic stability of the resulting closed-loop system under arbitrary switching laws. Based on the basic matrix inequality sufficient condition for checking the admissibility of switched singular systems,together with some matrix inequality convexifying techniques,the SOF controller synthesis is developed for the underlying systems. It is shown that the controller gains can be obtained by solving a set of strict linear matrix inequalities( LMIs). A simulation example is given to show the effectiveness of the proposed method.展开更多
The admissibility analysis and robust admissible control problem of the uncertain discrete-time switched linear singular (SLS) systems for arbitrary switching laws are investigated. Based on linear matrix inequalities...The admissibility analysis and robust admissible control problem of the uncertain discrete-time switched linear singular (SLS) systems for arbitrary switching laws are investigated. Based on linear matrix inequalities, some sufficient conditions are given for: A) the existence of generalized common Lyapunov solution and the admissibility of the SLS systems for arbitrary switching laws, B) the existence of static output feedback control laws ensuring the admissibility of the closed-loop SLS systems for arbitrary switching laws and norm-bounded uncertainties.展开更多
In this paper, we consider the design of interconnected H-infinity feedback control systems with quantized signals. We assume that a decentralized static output feedback has been designed for an interconnected continu...In this paper, we consider the design of interconnected H-infinity feedback control systems with quantized signals. We assume that a decentralized static output feedback has been designed for an interconnected continuous-time LTI system so that the closed-loop system is stable and a desired H-infinity disturbance attenuation level is achieved, and that the subsystems＇ measurement outputs are quantized before they are passed to the local controller. We propose a local-output-dependent strategy for updating the quantizers＇ parameters, so that the overall closed-loop system is asymptotically stable and achieves the same H-infinity disturbance attenuation level. Both the pre-designed controllers and the quantizers＇ parameters are constructed in a decentralized manner, depending on local information.展开更多
研究了区间二型模糊双线性系统的广义H_(2)控制问题。首先,设计新的李雅普诺夫泛函,采用静态输出反馈控制器,得到了确保闭环系统广义H_(2)稳定性的充分性条件;其次,利用序列线性规划矩阵(sequential linear programming matrix,SLPM)方...研究了区间二型模糊双线性系统的广义H_(2)控制问题。首先,设计新的李雅普诺夫泛函,采用静态输出反馈控制器,得到了确保闭环系统广义H_(2)稳定性的充分性条件;其次,利用序列线性规划矩阵(sequential linear programming matrix,SLPM)方法求解双线性矩阵不等式进行求解控制器增益;最后,通过一个数值例子验证了所得定理的正确性。展开更多
文摘This paper considers the design problem of static output feedback H ∞ controllers for descriptor linear systems with linear matrix inequality (LMI) approach. Necessary and sufficient conditions for the existence of a static output feedback H ∞ controller are given in terms of LMIs. Furthermore, the design method of H ∞ controllers is provided using the solutions to the LMIs.
基金Supported by the State Key Program of National Natural Science of China （60534010）, National Basic Research Program of China （973 Program）（2009CB320604）, National Natural Science Foundation of China （60674021）, the Funds for Creative Research Groups of China （60521003）, the 111 Project（B08015）, and the Funds of Ph.D. Program of Ministry of Eduction, China （20060145019）.
文摘Aim To study the optimal guaranteed cost control problem via static output feedback for uncertain linear discrete time systems with norm bounded parameter uncertainty in both the state and the control input matrices of the state space model. Methods\ An upper bound on a quadratic cost index was found for all admissible parameter uncertainties and minimized by using Lagrange multiplier approach. Results and Conclusion\ Sufficient conditions are given for the existence of a controller guaranteeing the closed loop system quadratic stability and providing an optimized bound. A numerical algorithm for solving the output feedback gain is also presented.
基金Project supported by the National Natural Science Foundation of China(Nos.11971303 and 11871330)。
文摘In this paper,the static output feedback stabilization for large-scale unstable second-order singular systems is investigated.First,the upper bound of all unstable eigenvalues of second-order singular systems is derived.Then,by using the argument principle,a computable stability criterion is proposed to check the stability of secondorder singular systems.Furthermore,by applying model reduction methods to original systems,a static output feedback design algorithm for stabilizing second-order singular systems is presented.A simulation example is provided to illustrate the effectiveness of the design algorithm.
基金This work was supported by National Outstanding Youth Science Foundation of China (No. 60025308)
文摘Based on a kind of regular form, a Lyapunov matrix with special structure is presented to design the sliding surface matrix conveniently and then an effective algorithm is developed on it. A simple static output feedback sliding mode control law without extra dynamic equation is given, such that the predefined sliding surface is reached in finite time for the general matching uncertainties. In the reported result, this extra dynamic equation is used for evaluating the norm bound of the unmeasured state vector. Finally, some examples are studied to illustrate the proposed approach.
基金Sponsored by the National Natural Science Foundation of China(Grant No.61004038)
文摘This paper is concerned with the problem of designing robust H∞and H2static output feedback controllers for a class of discrete-time piecewise-affine singular systems with norm-bounded time-varying parameters uncertainties. Based on a piecewise singular Lyapunov function combined with S-procedure,Projection lemma and some matrix inequality convexifying techniques,sufficient conditions in terms of linear matrix inequalities are given for the existence of an output-feedback controller for the discrete-time piecewiseaffine singular systems with a prescribed H∞disturbance attenuation level,and the H2norm is smaller than a given positive number. It is shown that the controller gains can be obtained by solving a family of LMIs parameterized by one or two scalar variables. The numerical examples are given to illustrate the effectiveness of the proposed design methods.
文摘The design of H∞ reduced order controllers is known to be a non-convex optimization problem for which no generic solution exists. In this paper, the use of Particle Swarm Optimization （PSO） for the computation of H~ static output feedbacks is investigated. Two approaches are tested. In a first part, a probabilistic-type PSO algorithm is defined for the computation of discrete sets of stabilizing static output feedback controllers. This method relies on a technique for random sample generation in a given domain. It is therefore used for computing a suboptimal Ha static output feedback solution, In a second part, the initial optimization problem is solved by PSO, the decision variables being the feedback gains. Results are compared with standard reduced order problem solvers using the COMPIeib （Constraint Matrix-optimization Problem Library） benchmark examples and appear to be much than satisfactory, proving the great potential of PSO techniques.
基金supported by the National Natural Science Foundation of China under Grant Nos.61134001,51477146the Applied Basic Research Program of Science and Technology Department of Sichuan Province,China under Grant No.2016JY0085
文摘This study is concerned with the stabilization issue of nonlinear systems subject to parameter uncertainties. An interval type-2 T-S fuzzy model is used to represent the nonlinear systems subject to parameter uncertainties. An interval type-2 fuzzy static output feedback controller is designed to synthesize the interval type-2 T-S fuzzy systems. The membership-function-dependent stability conditions are derived by utilizing the information of upper and lower membership functions. The proposed stability conditions are presented in the form of linear matrix inequalities（LMIs）. LMI-based stability conditions for interval type-2 fuzzy static output feedback H_∞ control synthesis are also developed.Several simulation examples are given to show the superiority of the proposed approach.
基金Supported by a grant from the Research Grants Council of the Hong Kong Special Administrative Region of China under Project CityU/112907
文摘This paper investigates the problem of robust exponential H∞ static output feedback controller design for a class of discrete-time switched linear systems with polytopic-type time-varying parametric uncertainties. The objective is to design a switched static output feedback controller guaranteeing the exponential stability of the resulting closed-loop system with a minimized exponential H∞ performance under average dwell-time switching scheme. Based on a parameter-dependent discontinuous switched Lyapunov function combined with Finsler＇s lemma and Dualization lemma, some novel conditions for exponential H∞ performance analysis are first proposed and in turn the static output feedback controller designs are developed. It is shown that the controller gains can be obtained by solving a set of linear matrix inequalities （LMIs）, which are numerically efficient with commercially available software. Finally, a simulation example is provided to illustrate the effectiveness of the proposed approaches.
基金Sponsored by the National Natural Science Foundation of China Grant No.61004038
文摘This paper is concerned with the problems of robust admissibility and static output feedback( SOF)stabilization for a class of discrete-time switched singular systems with norm-bounded parametric uncertainties.The objective is to design a suitable robust SOF controller guaranteeing the regularity,causality and asymptotic stability of the resulting closed-loop system under arbitrary switching laws. Based on the basic matrix inequality sufficient condition for checking the admissibility of switched singular systems,together with some matrix inequality convexifying techniques,the SOF controller synthesis is developed for the underlying systems. It is shown that the controller gains can be obtained by solving a set of strict linear matrix inequalities( LMIs). A simulation example is given to show the effectiveness of the proposed method.
基金Supported by National Natural Science Foundation of P. R. China (6022130, 60334040, 60428304)
文摘The admissibility analysis and robust admissible control problem of the uncertain discrete-time switched linear singular (SLS) systems for arbitrary switching laws are investigated. Based on linear matrix inequalities, some sufficient conditions are given for: A) the existence of generalized common Lyapunov solution and the admissibility of the SLS systems for arbitrary switching laws, B) the existence of static output feedback control laws ensuring the admissibility of the closed-loop SLS systems for arbitrary switching laws and norm-bounded uncertainties.
基金supported by the Japan Ministry of Education,Sciences and Culture under Grant-in-Aid for Scientific Research(C)(No.21560471)
文摘In this paper, we consider the design of interconnected H-infinity feedback control systems with quantized signals. We assume that a decentralized static output feedback has been designed for an interconnected continuous-time LTI system so that the closed-loop system is stable and a desired H-infinity disturbance attenuation level is achieved, and that the subsystems＇ measurement outputs are quantized before they are passed to the local controller. We propose a local-output-dependent strategy for updating the quantizers＇ parameters, so that the overall closed-loop system is asymptotically stable and achieves the same H-infinity disturbance attenuation level. Both the pre-designed controllers and the quantizers＇ parameters are constructed in a decentralized manner, depending on local information.
文摘研究了区间二型模糊双线性系统的广义H_(2)控制问题。首先,设计新的李雅普诺夫泛函,采用静态输出反馈控制器,得到了确保闭环系统广义H_(2)稳定性的充分性条件;其次,利用序列线性规划矩阵(sequential linear programming matrix,SLPM)方法求解双线性矩阵不等式进行求解控制器增益;最后,通过一个数值例子验证了所得定理的正确性。
