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Exponential mean-square stability of time-delay singular systems with Markovian switching and nonlinear perturbations. (English) Zbl 1370.34138

Summary: This paper considers exponential stability in mean-square of singular Markovian jump systems. The systems under consideration involve nonlinear perturbation and time-varying delays. By using the Lyapunov-Krasovskii functional, delay-dependent stability conditions in terms of linear matrix inequality (LMI) are addressed, which guarantee exponential mean-square stability and a prescribed \(H_{\infty}\) performance index for the considered systems. Two numerical examples are given to illustrate the effectiveness of the proposed main results.

MSC:

34K50 Stochastic functional-differential equations
34K32 Implicit functional-differential equations
34K27 Perturbations of functional-differential equations
34K20 Stability theory of functional-differential equations
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