Abstract
This paper addresses the problem of H∞ control of discrete-time linear systems with Markovian jumping parameters. The main contribution of the paper is to provide a method for designing a state-feedback H∞ control for systems where the jumping parameter is not accessible. The cases where the transition probability matrix of the Markov process is either exactly known, or unknown but belongs to a given polytope, are treated. The robust H∞ control problem for systems with polytopic-type uncertain state-space model matrices is also considered and a state-feedback control design based on a Lyapunov function that depends on the uncertain parameters is developed. The proposed control designs are given in terms of linear matrix inequalities. Illustrative numerical examples are provided to demonstrate the effectiveness of the derived results.
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