Discussion on: “An Algorithm for Solving a Perturbed Algebraic Riccati Equation”

Abstract

ATXþ XA XSXþQþ FðXÞ 1⁄4 0, with A,S,Q 2 R n being real matrices and F(X) representing a monotonically increasing operator in the positive semi-definite sense, U V ) FðUÞ FðVÞ. Riccati equations of this type appear in several control theory areas such as optimal control of linear systems with state dependent noise [3], mean square exponential stability of linear stochastic systems [4], minimax control of switched systems under sampling [5], and optimal control of jump parameter linear stochastic systems [6]. In [5,6], the linearly coupled systems of algebraic Riccati equations (CARE) were derived. It was shown in [1] that the CARE can be treated as a special case of the PARE. The algorithm of [1] for solving the above algebraic equation is based on ARE iterations of the form