New LMI methods to the robust control of discrete-time Markov jump linear systems

This paper treats the robust H₂ control of linear systems with Markov jump disturbances. The proposed approach is based upon the analysis of this class of systems via four adjoint operators. By means of new linear matrix inequality (LMI) characterizations of mean square stabilizing controllers, which include slack variables which to some extent separate the robustness and performance objectives, we introduce four alternative approaches to the design of controllers which are robustly stabilizing and at the same time provide a guaranteed level of H₂ performance. As an extension of the proposed methodology, we devise an iterative LMI technique to the design of robust H₂ controllers, whose convergence is guaranteed in a finite number of steps.