Robust Stability and Robust Stabilization of a Class of Discrete-Time Time-Varying Linear Stochastic Systems

2015 ◽  
Vol 53 (1) ◽  
pp. 30-57 ◽  
Author(s):  
Samir Aberkane ◽  
Vasile Dragan
Keyword(s):  
Robust Stability ◽  
Discrete Time ◽  
Stochastic Systems ◽  
Robust Stabilization ◽  
Time Varying ◽  
Linear Stochastic Systems

scholarly journals Robust Stabilization of Discrete-Time Systems with Time-Varying Delay: An LMI Approach

2008 ◽  
Vol 2008 ◽  
pp. 1-15 ◽  
Author(s):  
Valter J. S. Leite ◽  
Márcio F. Miranda
Keyword(s):  
Robust Stability ◽  
Discrete Time ◽  
Robust Stabilization ◽  
Linear Matrix ◽  
Time Varying ◽  
Time Varying Delay ◽  
Discrete Time Systems ◽  
Robust Stability Analysis ◽  
Time Systems ◽  
Varying Delay

Sufficient linear matrix inequality (LMI) conditions to verify the robust stability and to design robust state feedback gains for the class of linear discrete-time systems with time-varying delay and polytopic uncertainties are presented. The conditions are obtained through parameter-dependent Lyapunov-Krasovskii functionals and use some extra variables, which yield less conservative LMI conditions. Both problems, robust stability analysis and robust synthesis, are formulated as convex problems where all system matrices can be affected by uncertainty. Some numerical examples are presented to illustrate the advantages of the proposed LMI conditions.

scholarly journals New Results on Robust Stability and Stabilization of Linear Discrete-Time Stochastic Systems with Convex Polytopic Uncertainties

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
P. Niamsup ◽  
G. Rajchakit
Keyword(s):  
Robust Stability ◽  
Discrete Time ◽  
Stochastic Systems ◽  
Robust Stabilization ◽  
Linear Matrix ◽  
Polytopic Uncertainties ◽  
Delay Dependent ◽  
Parameter Dependent ◽  
Convex Polytopic Uncertainties ◽  
Robust Stability And Stabilization

This paper addresses the robust stability for a class of linear discrete-time stochastic systems with convex polytopic uncertainties. The system to be considered is subject to both interval time-varying delays and convex polytopic type uncertainties. Based on the augmented parameter-dependent Lyapunov-Krasovskii functional, new delay-dependent conditions for the robust stability are established in terms of linear matrix inequalities. An application to robust stabilization of linear discrete-time stochastic control systems is given. Numerical examples are included to illustrate the effectiveness of our results.

Robust stabilization of discrete-time linear systems with norm-bounded time-varying uncertainty

1994 ◽  
Vol 22 (5) ◽  
pp. 327-339 ◽  
Author(s):  
Germain Garcia ◽  
jacques Bernussou ◽  
Denis Arzelier
Keyword(s):  
Linear Systems ◽  
Discrete Time ◽  
Robust Stabilization ◽  
Time Varying ◽  
Time Linear

scholarly journals New Delay-Dependent Robust Stability Criterion for LPD Discrete-Time Systems with Interval Time-Varying Delays

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Narongsak Yotha ◽  
Kanit Mukdasai
Keyword(s):  
Robust Stability ◽  
Discrete Time ◽  
Model Transformation ◽  
Linear Matrix ◽  
Time Varying ◽  
Interval Time ◽  
Discrete Time Systems ◽  
Delay Dependent ◽  
Parameter Dependent ◽  
Time Systems

This paper investigates the problem of robust stability for linear parameter-dependent (LPD) discrete-time systems with interval time-varying delays. Based on the combination of model transformation, utilization of zero equation, and parameter-dependent Lyapunov-Krasovskii functional, new delay-dependent robust stability conditions are obtained and formulated in terms of linear matrix inequalities (LMIs). Numerical examples are given to demonstrate the effectiveness and less conservativeness of the proposed methods.

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