scholarly journals Exponential Stability and Robust H∞ Control for Discrete-Time Time-Delay Infinite Markov Jump Systems

2018 ◽  
Vol 2018 ◽  
pp. 1-9 ◽  
Author(s):  
Yueying Liu ◽  
Ting Hou
Keyword(s):  
Time Delay ◽  
Exponential Stability ◽  
Discrete Time ◽  
Stochastic Systems ◽  
Sufficient Conditions ◽  
Mean Square ◽  
Markov Jump ◽  
Multiplicative Noises ◽  
Exogenous Disturbance ◽  
Mean Square Exponential Stability

In this paper, exponential stability and robust H∞ control problem are investigated for a class of discrete-time time-delay stochastic systems with infinite Markov jump and multiplicative noises. The jumping parameters are modeled as an infinite-state Markov chain. By using a novel Lyapunov-Krasovskii functional, a new sufficient condition in terms of matrix inequalities is derived to guarantee the mean square exponential stability of the equilibrium point. Then some sufficient conditions for the existence of feedback controller are presented to guarantee that the resulting closed-loop system has mean square exponential stability for the zero exogenous disturbance and satisfies a prescribed H∞ performance level. Numerical simulations are exploited to validate the applicability of developed theoretical results.

scholarly journals Mean Square Exponential Stability of Stochastic Switched System with Interval Time-Varying Delays

2012 ◽  
Vol 2012 ◽  
pp. 1-12 ◽  
Author(s):  
Manlika Rajchakit ◽  
Grienggrai Rajchakit
Keyword(s):  
Time Delay ◽  
Exponential Stability ◽  
Stochastic System ◽  
Sufficient Conditions ◽  
Time Varying ◽  
Mean Square ◽  
Interval Time ◽  
Mean Square Exponential Stability ◽  
The Mean ◽  
Delay Dependent

This paper is concerned with mean square exponential stability of switched stochastic system with interval time-varying delays. The time delay is any continuous function belonging to a given interval, but not necessary to be differentiable. By constructing a suitable augmented Lyapunov-Krasovskii functional combined with Leibniz-Newton’s formula, a switching rule for the mean square exponential stability of switched stochastic system with interval time-varying delays and new delay-dependent sufficient conditions for the mean square exponential stability of the switched stochastic system are first established in terms of LMIs. Numerical example is given to show the effectiveness of the obtained result.

scholarly journals Exponential Stability of Stochastic Systems with Delay and Poisson Jumps

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Wenli Zhu ◽  
Jiexiang Huang ◽  
Zhao Zhao
Keyword(s):  
Time Delay ◽  
Exponential Stability ◽  
Stochastic Systems ◽  
Sufficient Conditions ◽  
Delay Systems ◽  
Mean Square ◽  
Poisson Jumps ◽  
Stochastic Delay ◽  
Exponentially Stable ◽  
The Mean

This paper focuses on the model of a class of nonlinear stochastic delay systems with Poisson jumps based on Lyapunov stability theory, stochastic analysis, and inequality technique. The existence and uniqueness of the adapted solution to such systems are proved by applying the fixed point theorem. By constructing a Lyapunov function and using Doob’s martingale inequality and Borel-Cantelli lemma, sufficient conditions are given to establish the exponential stability in the mean square of such systems, and we prove that the exponentially stable in the mean square of such systems implies the almost surely exponentially stable. The obtained results show that if stochastic systems is exponentially stable and the time delay is sufficiently small, then the corresponding stochastic delay systems with Poisson jumps will remain exponentially stable, and time delay upper limit is solved by using the obtained results when the system is exponentially stable, and they are more easily verified and applied in practice.

scholarly journals Stability Analysis and RobustH∞Control of Switched Stochastic Systems with Time-Varying Delay

2012 ◽  
Vol 2012 ◽  
pp. 1-17 ◽  
Author(s):  
Zhengrong Xiang ◽  
Guoxin Chen
Keyword(s):  
Exponential Stability ◽  
Stochastic Systems ◽  
Average Dwell Time ◽  
Linear Matrix ◽  
Time Varying ◽  
Mean Square ◽  
Time Varying Delay ◽  
Switched Stochastic Systems ◽  
Mean Square Exponential Stability ◽  
Varying Delay

The problems of mean-square exponential stability and robustH∞control of switched stochastic systems with time-varying delay are investigated in this paper. Based on the average dwell time method and Gronwall-Bellman inequality, a new mean-square exponential stability criterion of such system is derived in terms of linear matrix inequalities (LMIs). Then,H∞performance is studied and robustH∞controller is designed. Finally, a numerical example is given to illustrate the effectiveness of the proposed approach.

scholarly journals RobustH∞Control for Linear Stochastic Partial Differential Systems with Time Delay

2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
Xisheng Dai ◽  
Feiqi Deng ◽  
Jianxiang Zhang
Keyword(s):  
Time Delay ◽  
State Feedback ◽  
Sufficient Conditions ◽  
Delay Systems ◽  
Linear Matrix ◽  
Mean Square ◽  
Feedback Controllers ◽  
Partial Differential ◽  
Mean Square Exponential Stability ◽  
Linear Matrix Inequality Approach

This paper investigates the problems of robust stochastic mean square exponential stabilization and robustH∞for stochastic partial differential time delay systems. Sufficient conditions for the existence of state feedback controllers are proposed, which ensure mean square exponential stability of the resulting closed-loop system and reduce the effect of the disturbance input on the controlled output to a prescribed level ofH∞performance. A linear matrix inequality approach is employed to design the desired state feedback controllers. An illustrative example is provided to show the usefulness of the proposed technique.

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