Optimal Sampled-Data Control of Markov Jump Linear Systems through Differential LMIs

This paper addresses the problem of designing a sampled-data state feedback control law for continuous-time Markov jump linear systems (MJLS). The main goal is to characterize the optimal solution of this class of problems in the context of H-2 and H-infinity 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 associated to the time interval corresponding to two successive sampling instants. The design conditions are expressed through Differential Linear Matrix Inequalities (DLMI). The proposed method is simpler than those available in the literature to deal with this kind of systems since it is implemented without the necessity of an iterative algorithm. An example is solved for illustration.