Stability Analysis for a Class of Uncertain Discrete Singularly Perturbed Systems With Multiple Time Delays

2002 ◽  
Vol 124 (3) ◽  
pp. 467-472 ◽  
Author(s):  
Ching-Fa Chen ◽  
Shing-Tai Pan ◽  
Jer-Guang Hsieh
Keyword(s):  
Robust Stability ◽  
Stability Problem ◽  
Time Delays ◽  
Singularly Perturbed ◽  
Multiple Time ◽  
Singularly Perturbed Systems ◽  
Multiple Time Delays ◽  
Perturbed Linear Systems ◽  
Delay Dependent ◽  
Bounded Perturbations

In this paper, the robust stability problem for a class of nominally stable uncertain discrete singularly perturbed linear systems with multiple time delays is considered. A stability criterion for the slow and fast subsystems is first derived. A delay-dependent criterion is then proposed to guarantee the robust stability of the system subject to norm-bounded perturbations. A numerical example is provided to illustrate our main results.

Stability Analysis for a Class of Singularly Perturbed Systems With Multiple Time Delays

2004 ◽  
Vol 126 (3) ◽  
pp. 462-466 ◽  
Author(s):  
Shing-Tai Pan ◽  
Ching-Fa Chen ◽  
Jer-Guang Hsieh
Keyword(s):  
Asymptotic Stability ◽  
Time Delays ◽  
Original System ◽  
Singularly Perturbed ◽  
Multiple Time ◽  
Singularly Perturbed Systems ◽  
Fast Subsystem ◽  
Multiple Time Delays ◽  
Perturbed Systems ◽  
Slow Subsystem

The paper is to investigate the asymptotic stability for a general class of linear time-invariant singularly perturbed systems with multiple non-commensurate time delays. It is a common practice to investigate the asymptotic stability of the original system by establishing that of its slow subsystem and fast subsystem. A frequency-domain approach is first presented to determine a sufficient condition for the asymptotic stability of the slow subsystem (reduced-order model), which is a singular system with multiple time delays, and the fast subsystem. Two delay-dependent criteria, ε-dependent and ε-independent, are then proposed in terms of the H∞-norm for the asymptotic stability of the original system. Furthermore, a simple estimate of an upper bound ε* of singular perturbation parameter ε is proposed so that the original system is asymptotically stable for any ε∈0,ε*. Two numerical examples are provided to illustrate the use of our main results.

Delay-Dependent Stability Control for Power System With Multiple Time-Delays

2016 ◽  
Vol 31 (3) ◽  
pp. 2316-2326 ◽  
Author(s):  
Jian Li ◽  
Zhaohui Chen ◽  
Dongsheng Cai ◽  
Wei Zhen ◽  
Qi Huang
Keyword(s):  
Power System ◽  
Time Delays ◽  
Stability Control ◽  
Multiple Time ◽  
Multiple Time Delays ◽  
Delay Dependent ◽  
Delay Dependent Stability

scholarly journals Stability and stabilizability of dynamical systems with multiple time-varying delays: delay-dependent criteria

2003 ◽  
Vol 2003 (4) ◽  
pp. 137-152 ◽  
Author(s):  
D. Mehdi ◽  
E. K. Boukas
Keyword(s):  
Time Delays ◽  
Uncertain Systems ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Multiple Time ◽  
Multiple Time Delays ◽  
The Stability ◽  
Delay Dependent ◽  
Bounded Uncertainties ◽  
Norm Bounded Uncertainties

This paper deals with the class of uncertain systems with multiple time delays. The stability and stabilizability of this class of systems are considered. Their robustness are also studied when the norm-bounded uncertainties are considered. Linear matrix inequality (LMIs) delay-dependent sufficient conditions for both stability and stabilizability and their robustness are established to check if a system of this class is stable and/or is stabilizable. Some numerical examples are provided to show the usefulness of the proposed results.

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