Robust stability andH∞control for uncertain discrete Markovian jump singular systems with mode-dependent time-delay

2009 ◽  
Vol 19 (9) ◽  
pp. 965-985 ◽  
Author(s):  
Shuping Ma ◽  
Chenghui Zhang
Keyword(s):  
Time Delay ◽  
Robust Stability ◽  
Singular Systems ◽  
Markovian Jump

Robust stability for uncertain discrete singular systems with time-varying delays

2009 ◽  
Vol 223 (5) ◽  
pp. 713-720 ◽  
Author(s):  
Z Wu ◽  
H Su ◽  
J Chu
Keyword(s):  
Time Delay ◽  
Lyapunov Function ◽  
Robust Stability ◽  
Singular Systems ◽  
Time Varying ◽  
Numerical Example ◽  
Delay Bounds ◽  
Cross Terms ◽  
Discrete Singular Systems ◽  
Delay Dependent

This paper is concerned with the problem of delay-dependent robust stability for uncertain discrete singular systems with time-varying delays. Without introducing the free-weighting matrices to deal with the cross terms, a new and improved delay-dependent condition is established for the nominal systems to be regular, causal, and stable via a new Lyapunov function employing the integrated lower and upper time-delay bounds. The condition is also extended to the uncertain case. A numerical example is given to illustrate that the proposed methods are effective and lead to less conservatism than the existing ones.

scholarly journals Delay-dependent stability and stabilization of uncertain discrete-time markovian jump singular systems with time delay

2007 ◽  
Vol 49 (1) ◽  
pp. 111-129 ◽  
Author(s):  
Shuping Ma ◽  
Xinzhi Liu ◽  
Chenghui Zhang
Keyword(s):  
Time Delay ◽  
Linear Matrix Inequalities ◽  
Discrete Time ◽  
Stochastic Stability ◽  
Singular Systems ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Markovian Jump ◽  
Stability And Stabilization ◽  
Delay Dependent

This paper discusses robust stochastic stability and stabilization of time-delay discrete Markovian jump singular systems with parameter uncertainties. Based on the restricted system equivalent (RES) transformation, a delay-dependent linear matrix inequalities condition for time-delay discrete-time Markovian jump singular systems to be regular, causal and stochastically stable is established. With this condition, problems of robust stochastic stability and stabilization are solved, and delay-dependent linear matrix inequalities are obtained. A numerical example is also given to illustrate the effectiveness of this method.2000Mathematics subject classification: primary 39A12; secondary 93C55.

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