Stability and \(\mathcal H_\infty\) performance analysis for Markovian jump systems with time-varying delays. (English) Zbl 1395.93565
Summary: This paper is concerned with the problem of stability and \(\mathcal H_\infty\) performance analysis for Markovian jump systems with time-varying delays. By constructing a newly augmented Lyapunov-Krasovskii functional and utilizing some novel techniques which have not been proposed yet, a delay-dependent stability criterion with the framework of linear matrix inequalities (LMIs) is introduced in Theorem 1. Based on the result of Theorem 1, an \(\mathcal H_\infty\) performance analysis is conducted in Theorem 2. The effectiveness and superiority of the proposed theorems are illustrated via three numerical examples.
MSC:
| 93E15 | Stochastic stability in control theory |
| 93B36 | \(H^\infty\)-control |
| 60J75 | Jump processes (MSC2010) |
| 93E11 | Filtering in stochastic control theory |
| 93D30 | Lyapunov and storage functions |
Keywords:
stability; \(\mathcal H_\infty\) performance; Markovian jump systems; time-varying delays; Lyapunov-Krasovskii functionalReferences:
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