On input-to-state stability of systems with time-delay: A matrix inequalities approach

Nonlinear matrix inequalities (NLMIs) approach, which is known to be efficient for stability and L 2 -gain analysis, is extended to input-to-state stability (ISS). We first obtain sufficient conditions for ISS of systems with time-varying delays via Lyapunov–Krasovskii method. NLMIs are derived then...

Full description

Saved in:
Bibliographic Details
Published in:Automatica (Oxford) 2008-09, Vol.44 (9), p.2364-2369
Main Authors: Fridman, Emilia, Dambrine, Michel, Yeganefar, Nima
Format: Article
Language:English
Subjects:
Applied sciences
Computer science
control theory
systems
Control system analysis
Control theory. Systems
Exact sciences and technology
Input-to-state stability
LMI
Lyapunov–Krasovskii method
System theory
Time-delay systems
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:Nonlinear matrix inequalities (NLMIs) approach, which is known to be efficient for stability and L 2 -gain analysis, is extended to input-to-state stability (ISS). We first obtain sufficient conditions for ISS of systems with time-varying delays via Lyapunov–Krasovskii method. NLMIs are derived then for a class of systems with delayed state-feedback by using the S -procedure. If NLMIs are feasible for all x , then the results are global. When NLMIs are feasible in a compact set containing the origin, bounds on the initial state and on the disturbance are given, which lead to bounded solutions. The numerical examples of sampled-data quantized stabilization illustrate the efficiency of the method.
ISSN:0005-1098
1873-2836
DOI:10.1016/j.automatica.2008.01.012