Delay-dependent stability and hybrid L2×l2-gain analysis of linear impulsive time-delay systems: A continuous timer-dependent Lyapunov-like functional approach

Automatica ◽  
2020 ◽  
Vol 120 ◽  
pp. 109119 ◽  
Author(s):  
Wu-Hua Chen ◽  
Jialin Chen ◽  
Wei Xing Zheng
Keyword(s):  
Time Delay ◽  
Functional Approach ◽  
Delay Systems ◽  
Time Delay Systems ◽  
Delay Dependent ◽  
Delay Dependent Stability ◽  
L2 Gain

Stability of nonlinear time-delay systems satisfying a quadratic constraint

2016 ◽  
Vol 40 (3) ◽  
pp. 712-718 ◽  
Author(s):  
Mohsen Ekramian ◽  
Mohammad Ataei ◽  
Soroush Talebi
Keyword(s):  
Time Delay ◽  
Uncertain Systems ◽  
Delay Systems ◽  
Linear Matrix ◽  
Time Delay Systems ◽  
Matrix Inequalities ◽  
Quadratic Constraint ◽  
The Stability ◽  
Delay Dependent ◽  
Delay Dependent Stability

The stability problem of nonlinear time-delay systems is addressed. A quadratic constraint is employed to exploit the structure of nonlinearity in dynamical systems via a set of multiplier matrices. This yields less conservative results concerning stability analysis. By employing a Wirtinger-based inequality, a delay-dependent stability criterion is derived in terms of linear matrix inequalities for the nominal and uncertain systems. A numerical example is used to demonstrate the effectiveness of the proposed stability conditions in dealing with some larger class of nonlinearities.

scholarly journals Delay dependent stability of linear time-delay systems

2013 ◽  
Vol 40 (2) ◽  
pp. 223-245 ◽  
Author(s):  
Sreten Stojanovic ◽  
Dragutin Debeljkovic
Keyword(s):  
Time Delay ◽  
Large Scale ◽  
Linear Time ◽  
Direct Method ◽  
Sufficient Conditions ◽  
Lyapunov Equation ◽  
Delay Systems ◽  
Time Delay Systems ◽  
Delay Dependent ◽  
Delay Dependent Stability

This paper deals with the problem of delay dependent stability for both ordinary and large-scale time-delay systems. Some necessary and sufficient conditions for delay-dependent asymptotic stability of continuous and discrete linear time-delay systems are derived. These results have been extended to the large-scale time-delay systems covering the cases of two and multiple existing subsystems. The delay-dependent criteria are derived by Lyapunov's direct method and are exclusively based on the solvents of particular matrix equation and Lyapunov equation for non-delay systems. Obtained stability conditions do not possess conservatism. Numerical examples have been worked out to show the applicability of results derived.

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