An M-matrix approach to robust exponential stability of uncertain linear delay systems

2005 ◽  
Author(s):  
Bin Liu ◽  
Xiao-xin Liao ◽  
Xin-zhi Liu
Keyword(s):  
Exponential Stability ◽  
Delay Systems ◽  
Matrix Approach ◽  
Robust Exponential Stability ◽  
Linear Delay

Critical frequencies and parameters for linear delay systems: A Lyapunov matrix approach

2013 ◽  
Vol 62 (9) ◽  
pp. 781-790 ◽  
Author(s):  
Gilberto Ochoa ◽  
Vladimir L. Kharitonov ◽  
Sabine Mondié
Keyword(s):  
Delay Systems ◽  
Matrix Approach ◽  
Linear Delay ◽  
Lyapunov Matrix

ROBUST EXPONENTIAL STABILITY OF STOCHASTIC TIME-DELAY SYSTEMS WITH UNCERTAINTIES AND NONLINEAR PERTURBATIONS

2009 ◽  
Vol 06 (01) ◽  
pp. 61-71 ◽  
Author(s):  
HUAICHENG YAN ◽  
MAX Q.-H. MENG ◽  
XINHAN HUANG ◽  
HAO ZHANG
Keyword(s):  
Exponential Stability ◽  
Stochastic Systems ◽  
Sufficient Conditions ◽  
Delay Systems ◽  
Linear Matrix ◽  
Mean Square ◽  
Nonlinear Perturbations ◽  
Robust Exponential Stability ◽  
Mean Square Stability ◽  
Delay Dependent

In this paper, the delay-dependent robust exponential mean-square stability analysis problem is considered for a class of uncertain stochastic systems with time-varying delay and nonlinear perturbations. Some sufficient conditions on delay-dependent robust exponential stability in the mean square are established in terms of linear matrix inequalities (LMIs) by exploiting a novel Lyapunov–Krasovskii functional and by making use of zero equations methods. These developed results indicate less conservatism than the existing ones due to the introduction of some free weighting matrices which can be selected properly. The new delay-dependent stability criteria are expressed as a set of LMIs, which can be readily solved by using standard numerical software. Numerical examples are provided to demonstrate the effectiveness and the applicability of the proposed criteria.

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