TY - JOUR
T1 - On input-to-state stability of systems with time-delay
T2 - A matrix inequalities approach
AU - Fridman, Emilia
AU - Dambrine, Michel
AU - Yeganefar, Nima
PY - 2008/9
Y1 - 2008/9
N2 - Nonlinear matrix inequalities (NLMIs) approach, which is known to be efficient for stability and L2-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.
AB - Nonlinear matrix inequalities (NLMIs) approach, which is known to be efficient for stability and L2-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.
KW - Input-to-state stability
KW - LMI
KW - Lyapunov-Krasovskii method
KW - Time-delay systems
UR - http://www.scopus.com/inward/record.url?scp=50049134333&partnerID=8YFLogxK
U2 - 10.1016/j.automatica.2008.01.012
DO - 10.1016/j.automatica.2008.01.012
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AN - SCOPUS:50049134333
SN - 0005-1098
VL - 44
SP - 2364
EP - 2369
JO - Automatica
JF - Automatica
IS - 9
ER -