A Generalized Eigenvalue Approach for Solving Riccati Equations

Abstract

A numerically stable algorithm is derived to compute orthonormal bases for any deflating subspace of a regular pencil hB-A. The method is based on an update of the OZ-algorithm, in order to obtain any desired ordering of eigenvalues in the quasitriangular forms constructed by this algorithm. As applications we discuss a new approach to solve Riccati equations arising in linear system theory. The computation of deflating subspaces with specified spectrum is shown to be of crucial importance here.

Reverse-Engineering Existing Controllers for MPC Design

“…Note that (6) is a generalised Riccati equation, which can be solved by a numerically stabilised version of the MacFarlane-Potter algorithm (Laub, 1979;van Dooren, 1981). Its solution is not unique, but it is shown in that the corresponding optimal controller is unique, providing that the solution T is chosen so as to satisfy a standard regularity condition on the H 2 problem represented by (5).…”

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