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Stability and stabilization of continuous-time singular hybrid systems. (English) Zbl 1166.93365
Summary: The problems of stability and state feedback stabilization for a class of continuous-time singular hybrid systems are investigated. A new sufficient and necessary condition for a continuous-time singular hybrid system to be regular, impulse-free and stochastically stable is proposed in terms of a set of coupled strict linear matrix inequalities. Moreover, a new sufficient and necessary condition is presented for the existence of the state feedback controller in terms of a set of coupled strict matrix inequalities. Finally, a numerical example is given to illustrate the effectiveness of the obtained theoretical results.

MSC:
93D15 Stabilization of systems by feedback
60J75 Jump processes (MSC2010)
15A39 Linear inequalities of matrices
93E15 Stochastic stability in control theory
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