H∞ control for discrete‐time Markovian jump linear systems with partly unknown transition probabilities

In this paper, the problem of H∞ control for a class of discrete‐time Markovian jump linear system with partly unknown transition probabilities is investigated. The class of systems under consideration is more general, which covers the systems with completely known and completely unknown transition probabilities as two special cases. Moreover, in contrast to the uncertain transition probabilities studied recently, the concept of partly unknown transition probabilities proposed in this paper does not require any knowledge of the unknown elements. The H∞ controllers to be designed include state feedback and dynamic output feedback, since the latter covers the static one. The sufficient conditions for the existence of the desired controllers are derived within the matrix inequalities framework, and a cone complementary linearization algorithm is exploited to solve the latent equation constraints in the output‐feedback control case. Two numerical examples are provided to show the validness and potential of the developed theoretical results. Copyright © 2008 John Wiley & Sons, Ltd.

[1]  Umit Ozguner,et al.  Stability of linear feedback systems with random communication delays , 1994 .

[2]  L. Ghaoui,et al.  A cone complementarity linearization algorithm for static output-feedback and related problems , 1997, IEEE Trans. Autom. Control..

[3]  James Lam,et al.  Robust H∞ control of uncertain Markovian jump systems with time-delay , 2000, IEEE Trans. Autom. Control..

[4]  Zikuan Liu,et al.  Robust H∞ control of discrete-time Markovian jump linear systems with mode-dependent time-delays , 2001, IEEE Trans. Autom. Control..

[5]  Shengyuan Xu,et al.  Robust H∞ filtering for uncertain Markovian jump systems with mode-dependent time delays , 2003, IEEE Trans. Autom. Control..

[6]  Shengyuan Xu,et al.  Robust H∞ Filtering for a Class of Nonlinear Discrete-Time Markovian Jump Systems , 2004 .

[7]  Biao Huang,et al.  A new method for stabilization of networked control systems with random delays , 2005, Proceedings of the 2005, American Control Conference, 2005..

[8]  James Lam,et al.  On robust stabilization of Markovian jump systems with uncertain switching probabilities , 2005, Autom..

[9]  Shengyuan Xu,et al.  Robust H∞ control for uncertain discrete‐time stochastic bilinear systems with Markovian switching , 2005 .

[10]  Raja Sengupta,et al.  An H/sub /spl infin// approach to networked control , 2005, IEEE Transactions on Automatic Control.

[11]  Peng Shi,et al.  Transition probability bounds for the stochastic stability robustness of continuous- and discrete-time Markovian jump linear systems , 2006, Autom..

[12]  Huijun Gao,et al.  Robust H∞ filtering for switched linear discrete‐time systems with polytopic uncertainties , 2006 .