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\(\mathcal H_{\infty}\) stabilisation of switched linear stochastic systems under dwell time constraints. (English) Zbl 1417.93327

Summary: Based on the determination of a minimum dwell time, this article addresses the problem of characterising a switching strategy for \(\mathcal H_{\infty}\) stabilisation of switched linear stochastic systems with adapted external inputs. Sufficient conditions that assure exponential mean square stability and an \(\mathcal H_{\infty}\) performance index are established by analysing the time evolution of the second-order moment of the state and a recursive dynamic programming inequality, respectively. Alternative conditions are derived for numerical implementations. The proposed method is illustrated by numerical simulations.

MSC:

93E15 Stochastic stability in control theory
93C30 Control/observation systems governed by functional relations other than differential equations (such as hybrid and switching systems)
93E03 Stochastic systems in control theory (general)
93C05 Linear systems in control theory
93B36 \(H^\infty\)-control
90C39 Dynamic programming
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