Delay-Dependent Robust Stabilization and H ∞ Control for Nonlinear Stochastic Systems with Markovian Jump Parameters and Interval Time-Varying Delays

2011 ◽  
Vol 151 (1) ◽  
pp. 100-120 ◽  
Author(s):  
T. Senthilkumar ◽  
P. Balasubramaniam
Keyword(s):  
Stochastic Systems ◽  
Robust Stabilization ◽  
Time Varying ◽  
Markovian Jump ◽  
Nonlinear Stochastic Systems ◽  
Interval Time ◽  
Markovian Jump Parameters ◽  
Delay Dependent

scholarly journals Delay-Dependent Robust Exponential Stability for Uncertain Neutral Stochastic Systems with Interval Time-Varying Delay

2012 ◽  
Vol 2012 ◽  
pp. 1-22 ◽  
Author(s):  
Weihua Mao ◽  
Feiqi Deng ◽  
Anhua Wan
Keyword(s):  
Exponential Stability ◽  
Stochastic Systems ◽  
Linear Matrix ◽  
Time Varying ◽  
Mean Square ◽  
Robust Exponential Stability ◽  
Interval Time ◽  
Time Varying Delay ◽  
Mean Square Exponential Stability ◽  
Delay Dependent

This paper discusses the mean-square exponential stability of uncertain neutral linear stochastic systems with interval time-varying delays. A new augmented Lyapunov-Krasovskii functional (LKF) has been constructed to derive improved delay-dependent robust mean-square exponential stability criteria, which are forms of linear matrix inequalities (LMIs). By free-weight matrices method, the usual restriction that the stability conditions only bear slow-varying derivative of the delay is removed. Finally, numerical examples are provided to illustrate the effectiveness of the proposed method.

scholarly journals Stability analysis of uncertain stochastic systems with interval time-varying delays and nonlinear uncertainties via augmented Lyapunov functional

Filomat ◽  
2012 ◽  
Vol 26 (6) ◽  
pp. 1179-1188
Author(s):  
R. Jeetendra ◽  
Vernold Vivin
Keyword(s):  
Lyapunov Functional ◽  
Stochastic Systems ◽  
Linear Matrix ◽  
Time Varying ◽  
Lower And Upper Bounds ◽  
Parameter Uncertainties ◽  
Interval Time ◽  
Nonlinear Uncertainties ◽  
Delay Dependent ◽  
Delay Dependent Stability

In this work, the problem of delay-dependent stability for uncertain stochastic systems with interval time-varying delays and nonlinear uncertainties is addressed. The parameter uncertainties are assumed to be norm bounded and the delay is assumed to be time-varying and belong to a given interval, which means that the lower and upper bounds of interval time-varying delays are available. By constructing an augmented Lyapunov functional, a new delay interval-dependent stability criterion for the system is obtained in terms of Linear Matrix Inequalities (LMIs). Comparisons are made through numerical examples and less conservatism results are reported.

scholarly journals Robust Stability and Stabilization of a Class of Uncertain Nonlinear Discrete-Time Stochastic Systems with Interval Time-Varying Delays

2016 ◽  
Vol 2016 ◽  
pp. 1-13 ◽  
Author(s):  
Shuang Liang ◽  
Yali Dong
Keyword(s):  
Discrete Time ◽  
Stochastic Stability ◽  
Stochastic Systems ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Time Varying ◽  
Interval Time ◽  
Stochastic Stabilization ◽  
Stability And Stabilization ◽  
Delay Dependent

This paper deals with the problems of the robust stochastic stability and stabilization for a class of uncertain discrete-time stochastic systems with interval time-varying delays and nonlinear disturbances. By utilizing a new Lyapunov-Krasovskii functional and some well-known inequalities, some new delay-dependent criteria are developed to guarantee the robust stochastic stability of a class of uncertain discrete-time stochastic systems in terms of the linear matrix inequality (LMI). Then based on the state feedback controller, the delay-dependent sufficient conditions of robust stochastic stabilization for a class of uncertain discrete-time stochastic systems with interval time-varying delays are established. The controller gain is designed to ensure the robust stochastic stability of the closed-loop system. Finally, illustrative examples are given to demonstrate the effectiveness of the proposed method.

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