Optimal and Robust Sampled-Data Control of Markov Jump Linear Systems: A Differential LMI Approach

This paper addresses the problem of designing optimal sampled-data state feedback control for continuous-time Markov jump linear systems. Stability and performance robustness against polytopic uncertainty acting on the system parameters including the transition rate matrix are analyzed. The main goal is to characterize the optimal solution of this class of problems in the context of H
₂
and H
_∞
performances. The theoretical achievements are based on the direct application of the celebrated Bellman's Principle of Optimality expressed in terms of the dynamic programming equation applied to the time interval corresponding to two successive sampling instants. The design conditions are expressed through differential linear matrix inequalities. Examples are solved for illustration.