New methods for mode-independent robust control of Markov jump linear systems

This paper treats the H2H2 and H∞H∞ controls of linear systems with Markov jump disturbances, via new design methods based on linear matrix inequalities (LMIs). The proposed techniques are especially tailored to the scenario where the jump process cannot be measured, and apply to homogeneous Markov chains of any structure. In the scenario of polytopic uncertainty affecting the system matrices, new uncertainty-dependent methods are introduced for the design of robust controllers. Several numerical examples illustrate situations where the proposed techniques are less conservative than the ones found in the literature.