Generalized Riccati equations associated with guaranteed cost control: An overview of solutions and features

Robust control of dynamic linear systems with parametric uncertainties is based on the solution of generalized Riccati equations i.e. Riccati equations with additional terms depending on the uncertainties. In particular, guaranteed cost controller design requires the existence and computation of positive definite solutions of such equations. In the present paper, an overview of the Riccati equations arising in guaranteed cost control approaches is presented. It is shown that different uncertainty descriptions and the corresponding upper bounding functions lead to various forms of generalized Riccati equations that may admit either analytical or computational positive definite solutions. The associated closed-loop systems’ robustness features are also discussed.