H∞ robust and networked control of discrete-time MJLS through LMIs

This paper addresses the H∞ state-feedback control of Markov Jump Linear Systems (MJLS) through Linear Matrix Inequalities (LMIs). First, under the assumption that the Markov parameter is measured, the main contribution is on the LMI characterization of all linear feedback controllers such that the closed loop output remains bounded by a given norm level. This result allows the robust controller design to deal with convex bounded parameter uncertainty, probability uncertainty and cluster availability of the Markov mode. For partly unknown transition probabilities, the proposed design problem is proved to be less conservative than the one already available. For the case where each transition probability is considered unknown and belonging to a given interval, we also prove that our conditions are less conservative than a previous result from the literature. Under cluster availability of the Markov modes, we incorporate several models for measurement transmission network channels, such as the generalized Gilbert-Elliot, Fritchman or McCullough ones, into the MJLS framework. An example is solved for illustration and comparisons.