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SUMMARYThis paper deals with the control problem of discrete‐time Markov jump linear systems for the case in which the controller does not have access to the state of the Markov chain. A necessary optimal condition, which is nonlinear with respect to the optimizing variables, is introduced, and the corresponding solution is obtained through a variational convergent method. We illustrate the practical usefulness of the derived approach by applying it in the control speed of a real DC Motor device subject to abrupt power failures.Copyright © 2012 John Wiley & Sons, Ltd.

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In this paper we consider the full information discrete-time H -control problem ϱ for the class of linear systems with Markovian jumping parameters. The state-space of the Markov chain is assumed to take values in a countably infinite set. Full information here means that the controller has access to both the state-variables and jump-variables. A necessary and sufficient condition for the existence of a feedback controller that makes the l l -induced norm of the system less than a 2 prespecified bound is obtained. This condition is written in terms of a set of infinite coupled algebraic Riccati equations.

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