Mean-square exponential stability and stabilisation of stochastic singular systems with multiple time-varying delays. (English) Zbl 1341.93099
Summary: The stability and stabilization problems for a series of continuous stochastic singular systems with multiple time-varying delays are studied in this paper. First, a useful lemma is proposed and a delay-distribution-dependent Lyapunov functional is constructed. Then, a novel delay-distribution-dependent condition is given to ensure the unforced stochastic singular systems to be regular and impulse-free. The mean-square exponential stability of the whole system is guaranteed under the proposed lemma. As a result, a suitable feedback controller is designed via strict linear matrix inequality such that the system’s stabilization problem is guaranteed. Finally, numerical examples are illustrated to show the proposed result are less conservative than the existing ones and the potential of such technology.
MSC:
| 93E15 | Stochastic stability in control theory |
| 93D15 | Stabilization of systems by feedback |
| 93E03 | Stochastic systems in control theory (general) |
Keywords:
singular system; mean-square exponential stability; linear matrix inequality; \(\alpha\)-stability; robust controlReferences:
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