Abstract
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.
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