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Robust delay-range-dependent stabilization for Markovian jump systems with mode-dependent time delays and nonlinearities. (English) Zbl 1204.93104
Summary: This paper discusses the robust stabilization problem for a class of Markovian jump systems with nonlinear disturbances and time delays, which are time-varying in intervals and depend on system mode. By exploiting a new Lyapunov-Krasovskii functional, which takes into account the range of delay and by making use of novel techniques, a mean-square exponential stability result is proposed. Based on the obtained stability condition, a sufficient condition for state feedback controller which stabilizes the system and maximizes the bound on nonlinear perturbations is derived in terms of linear matrix inequalities involving a convex optimization. Finally, illustrative examples are presented to show the benefits and effectiveness of the proposed approaches.

MSC:
93D21 Adaptive or robust stabilization
93C10 Nonlinear systems in control theory
93D09 Robust stability
60J75 Jump processes (MSC2010)
93E03 Stochastic systems in control theory (general)
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