MINIMAX CONTROL OF DISTRIBUTED DISCRETE TIME SYSTEMS THROUGH SPECTRAL FACTORIZATION

We shall tie together three different problems: The firstproblem is the general question under which conditions a minimax control problem associated to \Phi can be solvedby a feedback law. The second problem is the existence of certain spectral factorization of the I/O-map of \Phi.The third problem is about certain solution of a Riccati equation system associated to \Phi. We shall show that these three problems are in factequivalent. This equivalence does not require any finite dimensional structure of the system \Phi. The I/O-stabilitynotion that we use throughout this paper is weaker than the conventional power stability (ae(A) < 1). Finally, con-nections to the existing power stable and finite dimensional theories are presented. 1 Introduction In this paper we study the nondefinite critical controlproblem in discrete time. Our basic object is a general H1transfer function whose input, state and output spaces ar