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Exponential Passification of Markovian Jump Nonlinear Systems with Partially Known Transition Rates

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  • Mengzhuo Luo
  • Shouming Zhong

Abstract

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.

Suggested Citation

  • Mengzhuo Luo & Shouming Zhong, 2012. "Exponential Passification of Markovian Jump Nonlinear Systems with Partially Known Transition Rates," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-24, March.
    • Handle: RePEc:hin:jnljam:950590
    DOI: 10.1155/2012/950590
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