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.

scholarly journals A Stability Condition with Delay-Dependence for a Class of Switched Large-Scale Time-Delay Systems

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Chi-Jo Wang ◽  
Juing-Shian Chiou
Keyword(s):  
Time Delay ◽  
Large Scale ◽  
Stability Margin ◽  
Delay Systems ◽  
Time Delay Systems ◽  
Switching Law ◽  
Delay Dependence ◽  
Delay Dependent ◽  
Delay Dependent Stability ◽  
Total Activation

By using the time-switched method and the comparison theorem, we derived a criterion of delay-dependent stability for the switched large-scale time-delay systems. To guarantee the exponential stability for the switched large-scale time-delay systems with stability marginλ, the total activation time ratio of the switching law is determined. An example is used to illustrate the effectiveness of our result.

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