Abstract
The optimal control problem for discrete time linear system subject to Markovian jumps in the paramrters is considered. The state space of the Markov chain is assumed to be infinite countable and the cost functional to be minimized is the infinite time horizon quadratic cost. It is shown that this optimintion problem is equivalent to the solution of an infinite countable set of coupled algebraic Riccati equations (ICARE). Sufficient conditions for existence and uniqueness of a positive semi-definite stabilizable solution to the ICARE are presented. These conditions are stated in terms of the concepts of stochastic stabilizability (SS) and stochastic detectability (SD).
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