This paper investigates Nash games for a class of linear stochastic systems governed by Itô’s differential equation with Markovian jump parameters both in finite-time horizon and infinite-time horizon.First,stoc...This paper investigates Nash games for a class of linear stochastic systems governed by Itô’s differential equation with Markovian jump parameters both in finite-time horizon and infinite-time horizon.First,stochastic Nash games are formulated by applying the results of indefinite stochastic linear quadratic(LQ)control problems.Second,in order to obtain Nash equilibrium strategies,crosscoupled stochastic Riccati differential(algebraic)equations(CSRDEs and CSRAEs)are derived.Moreover,in order to demonstrate the validity of the obtained results,stochastic H2/H∞control with state-and control-dependent noise is discussed as an immediate application.Finally,a numerical example is provided.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
This paper is concerned with state estimation problem for Markov jump linear systems where the disturbances involved in the systems equations and measurement equations are assumed to be Gaussian noise sequences.Based ...This paper is concerned with state estimation problem for Markov jump linear systems where the disturbances involved in the systems equations and measurement equations are assumed to be Gaussian noise sequences.Based on two properties of conditional expectation,orthogonal projective theorem is applied to the state estimation problem of the considered systems so that a novel suboptimal algorithm is obtained.The novelty of the algorithm lies in using orthogonal projective theorem instead of Kalman filters to estimate the state.A numerical comparison of the algorithm with the interacting multiple model algorithm is given to illustrate the effectiveness of the proposed algorithm.展开更多
Markov jump linear systems are defined as a family of linear systems with randomly Markov jumping parameters and are used to model systems subject to failures or changes in structure. The robust stabilization problem ...Markov jump linear systems are defined as a family of linear systems with randomly Markov jumping parameters and are used to model systems subject to failures or changes in structure. The robust stabilization problem of jump linear delay system with umcerratnty was studied. By using of linear matrix inequalities, the existence conditions of robust stabilizing and the state feedback controller designing methods are also presented and proved. Finally, an illustrated example shows the effectiveness of this approach.展开更多
This paper deals with the global exponential stability problems for stochastic neutral Markov jump systems （MJSs） with uncertain parameters and multiple time-delays. The delays are respectively considered as constan...This paper deals with the global exponential stability problems for stochastic neutral Markov jump systems （MJSs） with uncertain parameters and multiple time-delays. The delays are respectively considered as constant and time varying cases, and the uncertainties are assumed to be norm bounded. By selecting appropriate Lyapunov-Krasovskii functions, it gives the sufficient condition such that the uncertain neutral MJSs are globally exponentially stochastically stable for all admissible uncertainties. The stability criteria are formulated in the form of linear matrix inequalities （LMIs）, which can be easily checked in practice. Finally, two numerical examples are exploited to illustrate the effectiveness of the developed techniques.展开更多
The exponential passive filtering problem for a class of nonlinear Markov jump systems with uncertainties and time-delays is studied. The uncertain parameters are assumed unknown but norm bounded, and the nonlineariti...The exponential passive filtering problem for a class of nonlinear Markov jump systems with uncertainties and time-delays is studied. The uncertain parameters are assumed unknown but norm bounded, and the nonlinearities satisfy the quadratic condition. Based on the passive filtering theory, the sufficient condition for the existence of the mode-dependent passive filter is given by analyzing the reconstructed observer system. By using the appropriate Lyapnnov-Krasovskii function and applying linear matrix inequalities, the design scheme of the passive filter is derived and described as an optimization one. The presented exponential passive filter makes the error dynamic systems exponentially stochastically stable for all the admissible uncertainties, time-delays and nonlinearities, has the better abilities of state tracking and satisfies the given passive norm index. Simulation results demonstrate the validity of the proposed approach.展开更多
This study is concerned with the problem of finite-time H∞ filter design for uncertain discrete-time Markov Jump stochastic systems. Our attention is focused on the design of mode-dependent H∞ filter to ensure the f...This study is concerned with the problem of finite-time H∞ filter design for uncertain discrete-time Markov Jump stochastic systems. Our attention is focused on the design of mode-dependent H∞ filter to ensure the finite-time stability of the filtering error system and preserve a prescribed H∞ performance level for all admissible uncertainties. Sufficient conditions of filtering design for the system under consideration are developed and the corresponding filter parameters can be achieved in terms of linear matrix inequalities (LMI). Finally, a numerical example is provided to illustrate the validity of the proposed method.展开更多
The robust H∞ control problems for stochastic fuzzy neutral Markov jump systems（MJSs） with parameters uncertainties and multiple time-delays are considered.The delays are respectively considered as constant and tim...The robust H∞ control problems for stochastic fuzzy neutral Markov jump systems（MJSs） with parameters uncertainties and multiple time-delays are considered.The delays are respectively considered as constant and time varying,and the uncertain parameters are assumed to be norm bounded.By means of Takagi-Sugeno fuzzy models,the overall closed-loop fuzzy dynamics are constructed through selected membership functions.By selecting the appropriate Lyapunov-Krasovskii functions,the sufficient condition is given such that the uncertain fuzzy neutral MJSs are stochastically stability for all admissible uncertainties and satisfies the given H∞ control index.The stability and H∞ control criteria are formulated in the form of linear matrix inequalities,which can be easily checked in practice.Practical examples illustrate the effectiveness of the developed techniques.展开更多
The robust H∞ control for networked control systems with both stochastic network-induced delay and data packet dropout is studied. When data are transmitted over network, the stochastic data packet dropout process ca...The robust H∞ control for networked control systems with both stochastic network-induced delay and data packet dropout is studied. When data are transmitted over network, the stochastic data packet dropout process can be described by a two-state Markov chain. The networked control systems with stochastic network-induced delay and data packet dropout are modeled as a discrete time Markov jump linear system with two operation modes. The sufficient condition of robust H∞ control for networked control systems stabilized by state feedback controller is presented in terms of linear matrix inequality. The state feedback controller can be constructed via the solution of a set of linear matrix inequalities. An example is given to verify the effectiveness of the method proposed.展开更多
基金supported by the National Natural Science Foundation of China(No.71171061)China Postdoctoral Science Foundation(No.2014M552177)+2 种基金the Natural Science Foundation of Guangdong Province(No.S2011010004970)the Doctors Start-up Project of Guangdong University of Technology(No.13ZS0031)the 2014 Guangzhou Philosophy and Social Science Project(No.14Q21).
文摘This paper investigates Nash games for a class of linear stochastic systems governed by Itô’s differential equation with Markovian jump parameters both in finite-time horizon and infinite-time horizon.First,stochastic Nash games are formulated by applying the results of indefinite stochastic linear quadratic(LQ)control problems.Second,in order to obtain Nash equilibrium strategies,crosscoupled stochastic Riccati differential(algebraic)equations(CSRDEs and CSRAEs)are derived.Moreover,in order to demonstrate the validity of the obtained results,stochastic H2/H∞control with state-and control-dependent noise is discussed as an immediate application.Finally,a numerical example is provided.
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.
基金supported by the National Natural Science Foundation of China (No. 50977008,60521003,60774048)
文摘This paper is concerned with state estimation problem for Markov jump linear systems where the disturbances involved in the systems equations and measurement equations are assumed to be Gaussian noise sequences.Based on two properties of conditional expectation,orthogonal projective theorem is applied to the state estimation problem of the considered systems so that a novel suboptimal algorithm is obtained.The novelty of the algorithm lies in using orthogonal projective theorem instead of Kalman filters to estimate the state.A numerical comparison of the algorithm with the interacting multiple model algorithm is given to illustrate the effectiveness of the proposed algorithm.
文摘Markov jump linear systems are defined as a family of linear systems with randomly Markov jumping parameters and are used to model systems subject to failures or changes in structure. The robust stabilization problem of jump linear delay system with umcerratnty was studied. By using of linear matrix inequalities, the existence conditions of robust stabilizing and the state feedback controller designing methods are also presented and proved. Finally, an illustrated example shows the effectiveness of this approach.
基金supported by the National Natural Science Foundation of China (No.60574001)Program for New Century Excellent Talents in University (No.050485)Program for Innovative Research Team of Jiangnan University
文摘This paper deals with the global exponential stability problems for stochastic neutral Markov jump systems （MJSs） with uncertain parameters and multiple time-delays. The delays are respectively considered as constant and time varying cases, and the uncertainties are assumed to be norm bounded. By selecting appropriate Lyapunov-Krasovskii functions, it gives the sufficient condition such that the uncertain neutral MJSs are globally exponentially stochastically stable for all admissible uncertainties. The stability criteria are formulated in the form of linear matrix inequalities （LMIs）, which can be easily checked in practice. Finally, two numerical examples are exploited to illustrate the effectiveness of the developed techniques.
基金supported partly by the National Natural Science Foundation of China(60574001)the Program for New Century Excellent Talents in University(050485)the Program for Innovative Research Team of Jiangnan University.
文摘The exponential passive filtering problem for a class of nonlinear Markov jump systems with uncertainties and time-delays is studied. The uncertain parameters are assumed unknown but norm bounded, and the nonlinearities satisfy the quadratic condition. Based on the passive filtering theory, the sufficient condition for the existence of the mode-dependent passive filter is given by analyzing the reconstructed observer system. By using the appropriate Lyapnnov-Krasovskii function and applying linear matrix inequalities, the design scheme of the passive filter is derived and described as an optimization one. The presented exponential passive filter makes the error dynamic systems exponentially stochastically stable for all the admissible uncertainties, time-delays and nonlinearities, has the better abilities of state tracking and satisfies the given passive norm index. Simulation results demonstrate the validity of the proposed approach.
文摘This study is concerned with the problem of finite-time H∞ filter design for uncertain discrete-time Markov Jump stochastic systems. Our attention is focused on the design of mode-dependent H∞ filter to ensure the finite-time stability of the filtering error system and preserve a prescribed H∞ performance level for all admissible uncertainties. Sufficient conditions of filtering design for the system under consideration are developed and the corresponding filter parameters can be achieved in terms of linear matrix inequalities (LMI). Finally, a numerical example is provided to illustrate the validity of the proposed method.
基金supported by the National Natural Science Foundation of China (6097400160904045)+2 种基金the National Natural Science Foundation of Jiangsu Province (BK2009068)the Six Projects Sponsoring Talent Summits of Jiangsu Provincethe Program for Postgraduate Scientific Research and Innovation of Jiangsu Province
文摘The robust H∞ control problems for stochastic fuzzy neutral Markov jump systems（MJSs） with parameters uncertainties and multiple time-delays are considered.The delays are respectively considered as constant and time varying,and the uncertain parameters are assumed to be norm bounded.By means of Takagi-Sugeno fuzzy models,the overall closed-loop fuzzy dynamics are constructed through selected membership functions.By selecting the appropriate Lyapunov-Krasovskii functions,the sufficient condition is given such that the uncertain fuzzy neutral MJSs are stochastically stability for all admissible uncertainties and satisfies the given H∞ control index.The stability and H∞ control criteria are formulated in the form of linear matrix inequalities,which can be easily checked in practice.Practical examples illustrate the effectiveness of the developed techniques.
基金the National Science and the Technology Pursuit Project of China (2001BA204B01)
文摘The robust H∞ control for networked control systems with both stochastic network-induced delay and data packet dropout is studied. When data are transmitted over network, the stochastic data packet dropout process can be described by a two-state Markov chain. The networked control systems with stochastic network-induced delay and data packet dropout are modeled as a discrete time Markov jump linear system with two operation modes. The sufficient condition of robust H∞ control for networked control systems stabilized by state feedback controller is presented in terms of linear matrix inequality. The state feedback controller can be constructed via the solution of a set of linear matrix inequalities. An example is given to verify the effectiveness of the method proposed.
