Existence and uniqueness of unmixed solutions of the discrete-time algebraic Riccati equation

摘要

A solution X of a discrete-time algebraic Riccati equation is called unmixed if the corresponding closed-loop matrix Phi(X) has the property that the common roots of det(sI - Phi(X)) and det(I - sPhi(X)*) (if any) are on the unit circle. A necessary and sufficient condition is given for existence and uniqueness of an unmixed solution such that the eigenvalues of Phi(X) lie in a prescribed subset of C. (C) 2003 Elsevier B.V. All rights reserved. [References: 5]