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**Exponential passification of Markovian jump nonlinear systems with partially known transition rates.**
*(English)*
Zbl 1244.93175

Summary: The problems of delay-dependent exponential passivity analysis and exponential passification of uncertain Markovian jump systems (MJSs) with partially known transition rates are investigated. In the deterministic model, the time-varying delay is in a given range and the uncertainties are assumed to be norm bounded. With constructing appropriate Lyapunov-Krasovskii functional (LKF) combining with Jensen’s inequality and the free-weighting matrix method, delay-dependent exponential passification conditions are obtained in terms of linear matrix inequalities (LMI). Based on the condition, desired state-feedback controllers are designed, which guarantee that the closed-loop MJS is exponentially passive. Finally, a numerical example is given to illustrate the effectiveness of the proposed approach.

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\textit{M. Luo} and \textit{S. Zhong}, J. Appl. Math. 2012, Article ID 950590, 24 p. (2012; Zbl 1244.93175)

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