To study the design problem of robust reliable guaranteed cost controller for nonlinear singular stochastic systems, the Takagi-Sugeno （T-S） fuzzy model is used to represent a nonlinear singular stochastic system wi...To study the design problem of robust reliable guaranteed cost controller for nonlinear singular stochastic systems, the Takagi-Sugeno （T-S） fuzzy model is used to represent a nonlinear singular stochastic system with norm-bounded parameter uncertainties and time delay. Based on the linear matrix inequality （LMI） techniques and stability theory of stochastic differential equations, a stochastic Lyapunov function method is adopted to design a state feedback fuzzy controller. The resulting closed-loop fuzzy system is robustly reliable stochastically stable, and the corresponding quadratic cost function is guaranteed to be no more than a certain upper bound for all admissible uncertainties, as well as different actuator fault cases. A sufficient condition of existence and design method of robust reliable guaranteed cost controller is presented. Finally, a numerical simulation is given to illustrate the effectiveness of the proposed method.展开更多
This paper deals with the problem of H-infinity filter design for uncertain time-delay singular stochastic systems with Markovian jump. Based on the extended It6 stochastic differential formula, sufficient conditions ...This paper deals with the problem of H-infinity filter design for uncertain time-delay singular stochastic systems with Markovian jump. Based on the extended It6 stochastic differential formula, sufficient conditions for the solvability of these problems are obtained. Furthermore, It is shown that a desired filter can be constructed by solving a set of linear matrix inequalities. Finally, a simulation example is given to demonstrate the effectiveness of the proposed method.展开更多
In this paper, a state estimation problem in discrete\|time stochastic singular systems is investigated. It has been proved that the optimal state estimation problem of a discrete\|time stochastic singular system is e...In this paper, a state estimation problem in discrete\|time stochastic singular systems is investigated. It has been proved that the optimal state estimation problem of a discrete\|time stochastic singular system is equivalent to the optimal control problem of a deterministic singular system.展开更多
This paper deals with the problems of robust stochastic stabilization and H-infinity control for Markovian jump nonlinear singular systems with Wiener process via a fuzzy-control approach. The Takagi-Sugeno (T-S) fuzz...This paper deals with the problems of robust stochastic stabilization and H-infinity control for Markovian jump nonlinear singular systems with Wiener process via a fuzzy-control approach. The Takagi-Sugeno (T-S) fuzzy model is employed to represent a nonlinear singular system. The purpose of the robust stochastic stabilization problem is to design a state feedback fuzzy controller such that the closed-loop fuzzy system is robustly stochastically stable for all admissible uncertainties. In the robust H-infinity control problem, in addition to the stochastic stability requirement, a prescribed performance is required to be achieved. Linear matrix inequality (LMI) sufficient conditions are developed to solve these problems, respectively. The expressions of desired state feedback fuzzy controllers are given. Finally, a numerical simulation is given to illustrate the effectiveness of the proposed method.展开更多
Exact(approximate)controllability and exact(approximate)observability of stochastic singular systems in Banach spaces are discussed.Firstly,the condition for the existence and uniqueness of the mild solution to stocha...Exact(approximate)controllability and exact(approximate)observability of stochastic singular systems in Banach spaces are discussed.Firstly,the condition for the existence and uniqueness of the mild solution to stochastic singular systems is given by GE-semigroup in Banach spaces.Secondly,the necessary and sufficient conditions for the exact(approximate)controllability and exact(approximate)observability of the systems considered are derived in terms of GE-semigroup,and the dual principle is given.Thirdly,an illustrative example is given.展开更多
This paper discusses the impulse controllability and impulse observability of stochastic singular systems.Firstly,the condition for the existence and uniqueness of the impulse solution to stochastic singular systems i...This paper discusses the impulse controllability and impulse observability of stochastic singular systems.Firstly,the condition for the existence and uniqueness of the impulse solution to stochastic singular systems is given by Laplace transform.Secondly,the necessary and sufficient conditions for the impulse controllability and impulse observability of systems considered are derived in terms of matrix theory.Finally,an example is given to illustrate the effectiveness of the obtained theoretical results.展开更多
This paper deals with the delay-dependent stabilization problem for singular systems with Markovian jump parameters and time delays. A delay-dependent condition is established for the considered system to be regular, ...This paper deals with the delay-dependent stabilization problem for singular systems with Markovian jump parameters and time delays. A delay-dependent condition is established for the considered system to be regular, impulse free and stochastically stable. Based on the condition, a design algorithm of the desired state feedback controller which guarantees the resultant closed-loop system to be regular, impulse free and stochastically stable is proposed in terms of a set of strict linear matrix inequalities （LMIs）. Numerical examples show the effectiveness of the proposed methods.展开更多
基金the National Natural Science Foundation of China (60574088,60274014).
文摘To study the design problem of robust reliable guaranteed cost controller for nonlinear singular stochastic systems, the Takagi-Sugeno （T-S） fuzzy model is used to represent a nonlinear singular stochastic system with norm-bounded parameter uncertainties and time delay. Based on the linear matrix inequality （LMI） techniques and stability theory of stochastic differential equations, a stochastic Lyapunov function method is adopted to design a state feedback fuzzy controller. The resulting closed-loop fuzzy system is robustly reliable stochastically stable, and the corresponding quadratic cost function is guaranteed to be no more than a certain upper bound for all admissible uncertainties, as well as different actuator fault cases. A sufficient condition of existence and design method of robust reliable guaranteed cost controller is presented. Finally, a numerical simulation is given to illustrate the effectiveness of the proposed method.
基金This work was supported by the National Natural Science Foundation of China(No.60074007).
文摘This paper deals with the problem of H-infinity filter design for uncertain time-delay singular stochastic systems with Markovian jump. Based on the extended It6 stochastic differential formula, sufficient conditions for the solvability of these problems are obtained. Furthermore, It is shown that a desired filter can be constructed by solving a set of linear matrix inequalities. Finally, a simulation example is given to demonstrate the effectiveness of the proposed method.
文摘In this paper, a state estimation problem in discrete\|time stochastic singular systems is investigated. It has been proved that the optimal state estimation problem of a discrete\|time stochastic singular system is equivalent to the optimal control problem of a deterministic singular system.
基金supported by the National Natural Science Foundation of China (No.60574088, 60274014)the Research Plan Program of Scienceand Technology Ministry of Wuhan (No. 200950199019-07)
文摘This paper deals with the problems of robust stochastic stabilization and H-infinity control for Markovian jump nonlinear singular systems with Wiener process via a fuzzy-control approach. The Takagi-Sugeno (T-S) fuzzy model is employed to represent a nonlinear singular system. The purpose of the robust stochastic stabilization problem is to design a state feedback fuzzy controller such that the closed-loop fuzzy system is robustly stochastically stable for all admissible uncertainties. In the robust H-infinity control problem, in addition to the stochastic stability requirement, a prescribed performance is required to be achieved. Linear matrix inequality (LMI) sufficient conditions are developed to solve these problems, respectively. The expressions of desired state feedback fuzzy controllers are given. Finally, a numerical simulation is given to illustrate the effectiveness of the proposed method.
基金supported by the National Natural Science Foundation of China under Grant Nos.11926402 and 61973338。
文摘Exact(approximate)controllability and exact(approximate)observability of stochastic singular systems in Banach spaces are discussed.Firstly,the condition for the existence and uniqueness of the mild solution to stochastic singular systems is given by GE-semigroup in Banach spaces.Secondly,the necessary and sufficient conditions for the exact(approximate)controllability and exact(approximate)observability of the systems considered are derived in terms of GE-semigroup,and the dual principle is given.Thirdly,an illustrative example is given.
基金supported by the National Natural Science Foundation of China under Grant Nos.11926402and 61973338。
文摘This paper discusses the impulse controllability and impulse observability of stochastic singular systems.Firstly,the condition for the existence and uniqueness of the impulse solution to stochastic singular systems is given by Laplace transform.Secondly,the necessary and sufficient conditions for the impulse controllability and impulse observability of systems considered are derived in terms of matrix theory.Finally,an example is given to illustrate the effectiveness of the obtained theoretical results.
基金supported by the National Creative Research Groups Science Foundation of China (No.60721062)the National High Technology Research and Development Program of China (863 Program) (2006AA04 Z182)the National Natural Science Foundation of China (No.60736021)
文摘This paper deals with the delay-dependent stabilization problem for singular systems with Markovian jump parameters and time delays. A delay-dependent condition is established for the considered system to be regular, impulse free and stochastically stable. Based on the condition, a design algorithm of the desired state feedback controller which guarantees the resultant closed-loop system to be regular, impulse free and stochastically stable is proposed in terms of a set of strict linear matrix inequalities （LMIs）. Numerical examples show the effectiveness of the proposed methods.
