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 $\lambda B - A$. The method is based on an update of the $QZ$-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.