Suboptimal H2 and H∞ static output feedback control of hidden Markov jump linear systems

Abstract In this work we study the design of H 2 , H ∞ , and mixed H 2 / H ∞ static output feedback controllers for Markov jump linear systems in a context of partial information. We assume that the controller has only access to an observable variable that plays the role of a detector of the jump process. We present suboptimal conditions based on the so-called two step procedure in order to design static output feedback controllers that depend only on the detector such that the closed-loop system is stochastically stable and its H 2 or/and H ∞ norms are bounded. We also investigate the robust control case, in which the system matrices and transition probabilities are uncertain. An iterative algorithm that guarantees a non-increasing sequence of optimized costs is presented. Our results are illustrated by a numerical example in the context of systems subject to failures in which we show that the inherent conservatism of the mixed H 2 / H ∞ control and the two step procedure can be improved by the proposed method.

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