THE DISCRETE ALGEBRAIC RICCATI EQUATION AND LINEAR MATRIX INEQUALITY

We study the discrete time algebraic Riccati equation. In particular w e show that even in the most general cases there exists a one-one corr espondence between solutions of the algebraic Riccati equation and def lating subspaces of a matrix pencil. We also study the relationship be tween algebraic Riccati equation and the discrete time linear matrix i nequality. We show that in general only a subset of the set of rank-mi nimizing solutions of the linear matrix inequality correspond to the s olutions of the associated algebraic Riccati equation, and study under what conditions these sets are equal. In this process we also derive very weak assumptions under which a Riccati equation has a solution. ( C) 1998 Elsevier Science Inc.