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Robust stabilization for dynamic systems with multiple time-varying delays and nonlinear uncertainties. (English) Zbl 0981.93069
The author proves some new results dealing with the robust stabilization of uncertain systems with time delays using static state-feedback. The delays may be time-varying and multiple while there is no assumption on matching conditions for the uncertainties. The line of reasoning is based on the use of Lyapunov functionals and linear matrix inequalities. Two types of criteria for robust stabilization are considered. The first one, delay-independent, extends the results of [C.-H. Lien, J.-G. Hsieh and Y.-J. Sun, J. Math. Anal. Appl. 218, No. 2, 369-378 (1988; Zbl 0898.93028)] to problems with multiple time-varying delays and mismatched uncertainties. The second criterion, which is delay dependent, is less conservative and enables the estimation of the maximum admissible bound for the time delay, guaranteeing stabilization of the system. The results are illustrated by numerical examples solved using the Matlab LMI control toolbox.

MSC:
93D21 Adaptive or robust stabilization
93C23 Control/observation systems governed by functional-differential equations
93D30 Lyapunov and storage functions
Software:
LMI toolbox; Matlab
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