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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, John Wiley & Sons, vol. 2012(1).
    • Handle: RePEc:wly:jnljam:v:2012:y:2012:i:1:n:950590
    DOI: 10.1155/2012/950590
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    References listed on IDEAS

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    1. S. Xu & T. Chen & J. Lam, 2004. "Robust H ∞ Filtering for a Class of Nonlinear Discrete-Time Markovian Jump Systems," Journal of Optimization Theory and Applications, Springer, vol. 122(3), pages 651-668, September.
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