Full information H-infinity-control for discrete-time infinite Markov jump parameter systems

In this paper we consider the full information discrete-time H-infinity-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 the l(2)-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. (C) 1996 Academic Press, Inc.