Robust stability of singularly perturbed descriptor systems with uncertain Markovian switchings and nonlinear perturbations. (English) Zbl 1284.93180
Summary: This paper is concerned with the problem of robust stability of Markovian jump singularly perturbed descriptor systems with uncertain switchings and nonlinear perturbations for any \(\epsilon \in (0,\bar {\epsilon}]\), where \(\bar {\epsilon}\) is a pre-defined positive scalar. A linear matrix inequality (LMI) condition is firstly established to guarantee the existence and uniqueness of a solution. Then, an \(\epsilon\)-independent condition in terms of LMI related to \(\bar {\epsilon}\) is derived via using an \(\epsilon\)-dependent Lyapunov function, where the solution exists uniquely and is globally exponentially mean-square stable simultaneously. Finally, numerical examples are used to show the feasibility and effectiveness of the given theoretical results.
MSC:
| 93D09 | Robust stability |
| 93C70 | Time-scale analysis and singular perturbations in control/observation systems |
| 93C73 | Perturbations in control/observation systems |
| 60J75 | Jump processes (MSC2010) |
Keywords:
descriptor Markovian jump systems; singular perturbed descriptor systems; existence of solution; robust stability; uncertain Markovian switchingReferences:
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