ROBUST STABILITY AND STABILIZATION OF A CLASS OF SINGULAR SYSTEMS WITH MULTIPLE TIME-VARYING DELAYS

2005 ◽  
Vol 38 (1) ◽  
pp. 161-166 ◽  
Author(s):  
S.M. Saadni ◽  
M. Chaabane ◽  
D. Mehdi ◽  
O. Bachelier
Keyword(s):  
Robust Stability ◽  
Singular Systems ◽  
Multiple Time ◽  
Time Varying ◽  
Stability And Stabilization ◽  
Robust Stability And Stabilization

scholarly journals M-Matrix-Based Robust Stability and Stabilization Criteria for Uncertain Switched Nonlinear Systems with Multiple Time-Varying Delays

2021 ◽  
Vol 2021 ◽  
pp. 1-17
Author(s):  
Marwen Kermani ◽  
Anis Sakly
Keyword(s):  
Nonlinear Systems ◽  
Robust Stability ◽  
Feedback Stabilization ◽  
Linear Matrix ◽  
Multiple Time ◽  
Time Varying ◽  
Switched Nonlinear Systems ◽  
Aggregation Techniques ◽  
Stability And Stabilization ◽  
Robust Stability And Stabilization

This paper focuses on the robust stability and the memory feedback stabilization problems for a class of uncertain switched nonlinear systems with multiple time-varying delays. Especially, the considered time delays depend on the subsystem number. Based on a novel common Lyapunov functional, the aggregation techniques, and the Borne and Gentina criterion, new sufficient robust stability and stabilization conditions under arbitrary switching are established. Compared with existing results, the proposed criteria are explicit, simple to use, and obtained without finding a common Lyapunov function for all subsystems through linear matrix inequalities, considered very difficult in this situation. Moreover, compared with the memoryless one, the developed controller guarantees the robust stability of the corresponding closed-loop system with more performance by minimizing the effect of the delays in the system dynamics. Finally, two numerical simulation examples are shown to prove the practical utility and the effectiveness of the proposed theories.

Robust Stabilization of Stochastic Singular Systems with Markovian Switching

2012 ◽  
Vol 591-593 ◽  
pp. 1496-1501
Author(s):  
Yu Cai Ding ◽  
Hong Zhu ◽  
Yu Ping Zhang ◽  
Yong Zeng
Keyword(s):  
Robust Stability ◽  
Singular Systems ◽  
Robust Stabilization ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Parameter Uncertainties ◽  
Markovian Jump Parameters ◽  
Stochastic Disturbance ◽  
Stability And Stabilization ◽  
Robust Stability And Stabilization

In this paper, robust stability and stabilization of singular stochastic hybrid systems are investigated. The system under consideration involves parameter uncertainties, Itô-type stochastic disturbance, Markovian jump parameters as well as time-varying delays. The aim of this paper is to design a state controller such that the dynamic system is robust stable. By using the Lyapunov-Krasovskii functional and Itô's differential rule, delay-range-dependent sufficient conditions on robust stability and stabilization are obtained in the form of linear matrix inequalities (LMIs). A numerical example is given to illustrate the effectiveness of the proposed main results.

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