Linear Perturbation Theory for Structured Matrix Pencils Arising in Control Theory

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 penc...

Perturbation Theory for Rectangular Matrix Pencils Perturbation Theory for Rectangular Matrix Pencils

abstract The theory of eigenvalues and eigenvectors of rectangular matrix pencils is complicated by the fact that arbitrarily small perturbations of the pencil can cause them disappear. However, there are applications in which the properties of the pencil ensure the existence of eigen-values and eigenvectors. In this paper it is shown how to develop a perturbation theory for such pencils. ABSTR...

First order spectral perturbation theory of square singular matrix pencils

Let H(λ) = A0 + λA1 be a square singular matrix pencil, and let λ0 ∈ C be an eventually multiple eigenvalue of H(λ). It is known that arbitrarily small perturbations of H(λ) can move the eigenvalues of H(λ) anywhere in the complex plane, i.e., the eigenvalues are discontinuous functions of the entries of A0 and A1. Therefore, it is not possible to develop an eigenvalue perturbation theory for a...

Matrix Perturbation Theory

Ren-Cang Li University of Texas at Arlington 15.1 Eigenvalue Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15-1 15.2 Singular Value Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15-6 15.3 Polar Decomposition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15-7 15.4 Generalized Eigenvalue Problems . . . . . . . . . . . . . . . . . . . 15-...

Linear Control Theory and Structured Markov Chains