Full InformationH∞-Control for Discrete-Time Infinite Markov Jump Parameter Systems

AbstractIn this paper we consider the full information discrete-timeH∞-control problem 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 thel2-induced norm of the system less than a prespecified bound is obtained. This condition is written in terms of a set of infinite coupled algebraic Riccati equations