Exponential Stability of Discrete Time Delay Systems With Nonlinear Perturbations

2006 ◽  
Author(s):  
S. B. Stojanovic ◽  
D. Lj. Debeljkovic
Keyword(s):  
Exponential Stability ◽  
Direct Method ◽  
Delay Systems ◽  
Sufficient Condition ◽  
Time Delay Systems ◽  
Nonlinear Perturbations ◽  
Discrete Delay ◽  
Discrete Time Delay ◽  
Delay Dependent ◽  
Working Out

This paper gives sufficient condition for the exponential stability of discrete delay systems with nonlinear perturbations. This new, delay–dependent condition is derived using approach based on Lyapunov’s direct method. A numerical example has been working out to show the applicability of results derived.

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.

Stability Theory in the Sense of Lyapunov — Basic Approach: Discrete Singular Time Delayed System

Volume 1 ◽  
2004 ◽  
Author(s):  
D. Lj. Debeljkovic ◽  
S. A. Milinkovic ◽  
S. B. Stojanovic ◽  
M. B. Jovanovic
Keyword(s):  
Stability Theory ◽  
Direct Method ◽  
Sufficient Conditions ◽  
Delay Systems ◽  
Discrete Delay ◽  
Basic Approach ◽  
Delayed System ◽  
The Stability ◽  
Working Out ◽  
Singular Time

This paper gives sufficient conditions for the stability of linear singular discrete delay systems of the form Ex(k+1) = Aox(k)+A1x((k-1). These new, delay-independent conditions are derived using approach based on Lyapunov’s direct method. A numerical example has been working out to show the applicability of results derived. To the best knowledge of the authors, such result have not yet been reported.

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