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
A stabilization problem for stochastic systems with multiple input delays is investigated herein.A new method to construct an optimal control problem with input constraints is adopted.A sufficient stabilization condit...A stabilization problem for stochastic systems with multiple input delays is investigated herein.A new method to construct an optimal control problem with input constraints is adopted.A sufficient stabilization condition is established via Riccati-type equations,whose verification is computationally simple because the variable dimension of the equations does not increase with regard to the delay.A stabilization controller is proposed,and it is a feedback of the state and a history input.This controller uses less history information than those with distributed terms.Two numerical examples illustrate the effectiveness of the obtained results.展开更多
This paper is concerned with the H_∞ control problem for a class of nonlinear stochastic Markov jump systems with time-delay and system state-, control input-and external disturbancedependent noise. Firstly, by solvi...This paper is concerned with the H_∞ control problem for a class of nonlinear stochastic Markov jump systems with time-delay and system state-, control input-and external disturbancedependent noise. Firstly, by solving a set of Hamilton-Jacobi inequalities(HJIs), the exponential mean square H_∞ controller design of delayed nonlinear stochastic Markov systems is presented. Secondly,by using fuzzy T-S model approach, the H_∞ controller can be designed via solving a set of linear matrix inequalities(LMIs) instead of HJIs. Finally, two numerical examples are provided to show the effectiveness of the proposed design methods.展开更多
This paper is concerned with partially-observed optimal control problems for stochastic delay systems. Combining Girsanov's theorem with a standard variational technique, the authors obtain a maximum principle on ...This paper is concerned with partially-observed optimal control problems for stochastic delay systems. Combining Girsanov's theorem with a standard variational technique, the authors obtain a maximum principle on the assumption that the system equation contains time delay and the control domain is convex. The related adjoint processes are characterized as solutions to anticipated backward stochastic differential equations in finite-dimensional spaces. Then, the proposed theoretical result is applied to study partially-observed linear-quadratic optimal control problem for stochastic delay system and an explicit observable control variable is given.展开更多
This paper treats the feedback stabilization of nonlinear stochastic time-delay systems with state and control-dependent noise. Some locally （globally） robustly stabilizable conditions are given in terms of matrix i...This paper treats the feedback stabilization of nonlinear stochastic time-delay systems with state and control-dependent noise. Some locally （globally） robustly stabilizable conditions are given in terms of matrix inequalities that are independent of the delay size. When it is applied to linear stochastic time-delay systems, sufficient conditions for the state-feedback stabilization are presented via linear matrix inequalities. Several previous results are extended to more general systems with both state and control-dependent noise, and easy computation algorithms are also given.展开更多
This paper considers the problem of stochastic stabilization and energy-to-peak control for a class of discrete stochastic fuzzy systems with interval time-delays. The objective is to design a state feedback controlle...This paper considers the problem of stochastic stabilization and energy-to-peak control for a class of discrete stochastic fuzzy systems with interval time-delays. The objective is to design a state feedback controller such that the closed-loop system is stochastic stable and satisfies energy-to-peak performance. Based on the idea of interval partitioning, some new sufficient conditions are presented in LMI.展开更多
In recent years, the stability of hybrid stochastic delay systems, one of the important issues in the study of stochastic systems, has received considerable attention. However, the existing results do not deal with th...In recent years, the stability of hybrid stochastic delay systems, one of the important issues in the study of stochastic systems, has received considerable attention. However, the existing results do not deal with the structure of the diffusion but estimate its upper bound, which induces conservatism. This paper studies delay-dependent robust stability of hybrid stochastic delay systems. A delay-dependent criterion for robust exponential stability of hybrid stochastic delay systems is presented in terms of linear matrix inequalities （LMIs）, which exploits the structure of the diffusion. Numerical examples are given to verify the effectiveness and less conservativeness of the proposed method.展开更多
The robust guaranteed cost filtering problem for a dass of linear uncertain stochastic systems with time delays is investigated. The system under study involves time delays, jumping parameters and Brownian motions. Th...The robust guaranteed cost filtering problem for a dass of linear uncertain stochastic systems with time delays is investigated. The system under study involves time delays, jumping parameters and Brownian motions. The transition of the jumping parameters in systems is governed by a finite-state Markov process. The objective is to design linear memoryless filters such that for all uncertainties, the resulting augmented system is robust stochastically stable independent of delays and satisfies the proposed guaranteed cost performance. Based on stability theory in stochastic differential equations, a sufficient condition on the existence of robust guaranteed cost filters is derived. Robust guaranteed cost filters are designed in terms of linear matrix inequalities. A convex optimization problem with LMI constraints is formulated to design the suboptimal guaranteed cost filters.展开更多
Based on the definition of passivity extended from deterministic system, the sufficient condition on passivity of stochastic jump system is given against unknown state time delay. By means of memoryless state feedback...Based on the definition of passivity extended from deterministic system, the sufficient condition on passivity of stochastic jump system is given against unknown state time delay. By means of memoryless state feedback, a class of state delayed stochastic jump systems may be led to passive. The feedback controllers are mode-dependent and can be constructed in terms of the solutions of a set of coupled linear matrix inequalities. A numerical example illustrates the results.展开更多
The problem of delay-dependent exponential stability is investigated for impulsive stochastic systems with time-varying delay. Although the exponential stability of impulsive stochastic delay systems has been discusse...The problem of delay-dependent exponential stability is investigated for impulsive stochastic systems with time-varying delay. Although the exponential stability of impulsive stochastic delay systems has been discussed by several authors, few works have been done on delay-dependent exponential stability of impulsive stochastic delay systems. Firstly, the Lyapunov-Krasovskii functional method combing the free-weighting matrix approach is applied to investigate this problem. Some delay-dependent mean square exponential stability criteria are derived in terms of linear matrix inequalities. In particular, the estimate of the exponential convergence rate is also provided, which depends on system parameters and impulsive effects. The obtained results show that the system will stable if the impulses＇ frequency and amplitude are suitably related to the increase or decrease of the continuous flows, and impulses may be used as controllers to stabilize the underlying stochastic system. Numerical examples are given to show the effectiveness of the results.展开更多
The mean-square exponential stability problem is investigated for a class of stochastic time-varying delay systems with Markovian jumping parameters. By decomposing the delay interval into multiple equidistant subinte...The mean-square exponential stability problem is investigated for a class of stochastic time-varying delay systems with Markovian jumping parameters. By decomposing the delay interval into multiple equidistant subintervals, a new delay-dependent and decay-rate-dependent criterion is presented based on constructing a novel Lyapunov functional and employing stochastic analysis technique. Besides, the decay rate has no conventional constraint and can be selected according to different practical conditions. Finally, two numerical examples are provided to show that the obtained result has less conservatism than some existing ones in the literature.展开更多
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.
基金supported by Shandong Provincial Natural Science Foundation of China under Grant Nos.ZR2022MF239 and ZR2021MA002。
文摘A stabilization problem for stochastic systems with multiple input delays is investigated herein.A new method to construct an optimal control problem with input constraints is adopted.A sufficient stabilization condition is established via Riccati-type equations,whose verification is computationally simple because the variable dimension of the equations does not increase with regard to the delay.A stabilization controller is proposed,and it is a feedback of the state and a history input.This controller uses less history information than those with distributed terms.Two numerical examples illustrate the effectiveness of the obtained results.
基金supported by the National Natural Science Foundation of China under Grant Nos.61573227,61633014the Natural Science Foundation of Shandong Province of China under Grant No.2013ZRE28089+2 种基金the Research Fund for the Taishan Scholar Project of Shandong Province of ChinaSDUST Research Fund under Grant No.2015TDJH105 State Key Laboratory of Alternate Electrical Power System with Renewable Energy Sources under Grant No.LAPS16011
文摘This paper is concerned with the H_∞ control problem for a class of nonlinear stochastic Markov jump systems with time-delay and system state-, control input-and external disturbancedependent noise. Firstly, by solving a set of Hamilton-Jacobi inequalities(HJIs), the exponential mean square H_∞ controller design of delayed nonlinear stochastic Markov systems is presented. Secondly,by using fuzzy T-S model approach, the H_∞ controller can be designed via solving a set of linear matrix inequalities(LMIs) instead of HJIs. Finally, two numerical examples are provided to show the effectiveness of the proposed design methods.
文摘This paper is concerned with partially-observed optimal control problems for stochastic delay systems. Combining Girsanov's theorem with a standard variational technique, the authors obtain a maximum principle on the assumption that the system equation contains time delay and the control domain is convex. The related adjoint processes are characterized as solutions to anticipated backward stochastic differential equations in finite-dimensional spaces. Then, the proposed theoretical result is applied to study partially-observed linear-quadratic optimal control problem for stochastic delay system and an explicit observable control variable is given.
基金This work was supported by the National Natural Science Foundation of China(No.60474013)Specialized Research Fund for the Doctoral Program of Higher Education (No. 20050424002)the Doctoral Foundation of Shandong Province (No. 2004BS01010)
文摘This paper treats the feedback stabilization of nonlinear stochastic time-delay systems with state and control-dependent noise. Some locally （globally） robustly stabilizable conditions are given in terms of matrix inequalities that are independent of the delay size. When it is applied to linear stochastic time-delay systems, sufficient conditions for the state-feedback stabilization are presented via linear matrix inequalities. Several previous results are extended to more general systems with both state and control-dependent noise, and easy computation algorithms are also given.
基金supported by the National Natural Science Foundation of China (No. 61004046)the China Postdoctoral Science Foundation (No.20110491336)+1 种基金the Postdoctoral Science Foundation of Jiangsu Province (No. 1001007C)the Young and Middle-Aged Scientists Research Awards Fund of Shandong Province (No. 2009BSB01450)
文摘This paper considers the problem of stochastic stabilization and energy-to-peak control for a class of discrete stochastic fuzzy systems with interval time-delays. The objective is to design a state feedback controller such that the closed-loop system is stochastic stable and satisfies energy-to-peak performance. Based on the idea of interval partitioning, some new sufficient conditions are presented in LMI.
文摘In recent years, the stability of hybrid stochastic delay systems, one of the important issues in the study of stochastic systems, has received considerable attention. However, the existing results do not deal with the structure of the diffusion but estimate its upper bound, which induces conservatism. This paper studies delay-dependent robust stability of hybrid stochastic delay systems. A delay-dependent criterion for robust exponential stability of hybrid stochastic delay systems is presented in terms of linear matrix inequalities （LMIs）, which exploits the structure of the diffusion. Numerical examples are given to verify the effectiveness and less conservativeness of the proposed method.
文摘The robust guaranteed cost filtering problem for a dass of linear uncertain stochastic systems with time delays is investigated. The system under study involves time delays, jumping parameters and Brownian motions. The transition of the jumping parameters in systems is governed by a finite-state Markov process. The objective is to design linear memoryless filters such that for all uncertainties, the resulting augmented system is robust stochastically stable independent of delays and satisfies the proposed guaranteed cost performance. Based on stability theory in stochastic differential equations, a sufficient condition on the existence of robust guaranteed cost filters is derived. Robust guaranteed cost filters are designed in terms of linear matrix inequalities. A convex optimization problem with LMI constraints is formulated to design the suboptimal guaranteed cost filters.
文摘Based on the definition of passivity extended from deterministic system, the sufficient condition on passivity of stochastic jump system is given against unknown state time delay. By means of memoryless state feedback, a class of state delayed stochastic jump systems may be led to passive. The feedback controllers are mode-dependent and can be constructed in terms of the solutions of a set of coupled linear matrix inequalities. A numerical example illustrates the results.
基金supported by the National Natural Science Foundation of China (60874114)the Fundamental Research Funds for the Central Universities, South China University of Technology (SCUT)(2009ZM0140)
文摘The problem of delay-dependent exponential stability is investigated for impulsive stochastic systems with time-varying delay. Although the exponential stability of impulsive stochastic delay systems has been discussed by several authors, few works have been done on delay-dependent exponential stability of impulsive stochastic delay systems. Firstly, the Lyapunov-Krasovskii functional method combing the free-weighting matrix approach is applied to investigate this problem. Some delay-dependent mean square exponential stability criteria are derived in terms of linear matrix inequalities. In particular, the estimate of the exponential convergence rate is also provided, which depends on system parameters and impulsive effects. The obtained results show that the system will stable if the impulses＇ frequency and amplitude are suitably related to the increase or decrease of the continuous flows, and impulses may be used as controllers to stabilize the underlying stochastic system. Numerical examples are given to show the effectiveness of the results.
基金supported by the Program for New Century Excellent Talents in University, the Graduate Innovation Program of Jiangsu Province (CX06B-051Z)the Scientific Research Foundation of Graduate School of Southeast University (YBJJ0929)
文摘The mean-square exponential stability problem is investigated for a class of stochastic time-varying delay systems with Markovian jumping parameters. By decomposing the delay interval into multiple equidistant subintervals, a new delay-dependent and decay-rate-dependent criterion is presented based on constructing a novel Lyapunov functional and employing stochastic analysis technique. Besides, the decay rate has no conventional constraint and can be selected according to different practical conditions. Finally, two numerical examples are provided to show that the obtained result has less conservatism than some existing ones in the literature.
