Linear Perturbation Theory for Structured Matrix Pencils Arising in Control Theory

We investigate the effect of linear perturbations on several structured matrix pencils arising in control theory. These include skew-symmetric/symmetric pencils arising in the computation of optimal H∞ control and linear quadratic control for continuous and discrete time systems. 1. Introduction. In this paper we study the effects of linear perturbations on the spectra of structured matrix pencils arising in control theory. The results that we present complement and generalize general perturbation results for Hamiltonian matrices as they were recently studied in [14] and we also extend results in [21, 22, 23]. Our main motivation arises from the following classical problems in optimal and robust control. Consider a linear constant coefficient dynamical system of the form