A NOTE ON EXTENDED ALGEBRAIC RICCATI EQUATIONS APPEARING IN DISSIPATIVITY THEORY

摘要

Necessary and sufficient conditions for existence of a solution to a new class of extended algebraic Riccati equations (ARE) are presented. The class, which is of interest in general dissipativity theory, and in particular in robust H_∞ control, contains arbitrary―possibly singular―quadratic term and possibly degenerate frequency domain function. Instrumental to establish our results is the analysis of a particular matrix pencil associated with the extended ARE that was recently introduced by Ionescu and Weiss. The conditions for existence of solutions of the extended ARE―including stabilizing solutions―are formulated in terms of this pencil.