Robust sampled-data control for Markovian jump linear systems

In this paper, we consider the problem of robust control for uncertain sampled-data systems that possess random jumping parameters which is described by a finite-state Markov process. The conditions for the existence of a stabilizing control and optimal control for the underlying systems are obtained. The desired controllers are designed which are in terms of matrix inequalities. Finally, a numerical example is given to show the potential of the proposed techniques.

[1]  M. Basin,et al.  OPTIMAL STATE ESTIMATION FOR CONTINUOUS STOCHASTIC STATE-SPACE SYSTEM WITH HYBRID MEASUREMENTS , 2006 .

[2]  Yuanqing Xia,et al.  On designing of sliding-mode control for stochastic jump systems , 2006, IEEE Transactions on Automatic Control.

[3]  R. P. Marques,et al.  Mixed H2/H∞-control of discrete-time Markovian jump linear systems , 1998, IEEE Trans. Autom. Control..

[4]  Biao Huang,et al.  Robust digital model predictive control for linear uncertain systems with saturations , 2004, IEEE Trans. Autom. Control..

[5]  K. Loparo,et al.  Stochastic stability properties of jump linear systems , 1992 .

[6]  E. Boukas,et al.  Delay-dependent stability and output feedback stabilisation of Markov jump system with time-delay , 2002 .

[7]  Bruce A. Francis,et al.  Optimal Sampled-Data Control Systems , 1996, Communications and Control Engineering Series.

[8]  R. P. Marques,et al.  Mixed H2/H∞-control of discrete-time Markovian jump linear systems , 1998, IEEE Trans. Autom. Control..

[9]  James Lam,et al.  A linear matrix inequality (LMI) approach to robust H/sub 2/ sampled-data control for linear uncertain systems. , 2003, IEEE transactions on systems, man, and cybernetics. Part B, Cybernetics : a publication of the IEEE Systems, Man, and Cybernetics Society.

[10]  El-Kébir Boukas,et al.  Stabilization of Stochastic Nonlinear Hybrid Systems , 2005 .

[11]  Peng Shi,et al.  Control of Markovian jump discrete-time systems with norm bounded uncertainty and unknown delay , 1999, IEEE Trans. Autom. Control..

[12]  L. Ghaoui,et al.  A cone complementarity linearization algorithm for static output-feedback and related problems , 1996, Proceedings of Joint Conference on Control Applications Intelligent Control and Computer Aided Control System Design.