Robust Stability and Control of Uncertain Discrete-Time Markov Jump Linear Systems

This paper deals with robust stability and control of uncertain discrete-time linear systems with Markovian jumping parameters. Systems with polytopic-type parameter uncertainty in either the state-space model matrices, or in the transition probability matrix of the Markov process, are considered. This paper develops new methods of robust stability analysis and robust stabilization in the mean square sense which are dependent on the system uncertainty. The design of both mode-dependent and mode-independent control laws is addressed. The proposed methods are given in terms of linear matrix inequalities. Illustrative numerical examples are provided to demonstrate the effectiveness of the derived results