ℋ2 state feedback sampled-data control for Markov Jump Linear Systems

This paper is entirely devoted to analyzing the ℋ₂ optimal state feedback sampled-data control design problem for Markov Jump Linear Systems. Our propose is to search for a solution to this problem by imbedding it in a more general class of dynamical systems, which we call Hybrid Markov Jump Linear System (HMJLS). In this new and wide context, we show how to calculate a sampled-data state feedback control that minimizes the ℋ₂ performance index associated to the closed-loop system from the solution of a specific two-point boundary value problem. This result is adapted to provide optimal control conditions based on linear matrix inequalities (LMIs). The theory is illustrated by means of an academical example.