Structured eigenvalue/eigenvector backward errors of matrix pencils arising in optimal control

Structured Eigenvalue Backward Errors of Matrix Pencils and Polynomials with Palindromic Structures

We derive formulas for the backward error of an approximate eigenvalue of a ∗palindromic matrix polynomial with respect to ∗-palindromic perturbations. Such formulas are also obtained for complex T -palindromic pencils and quadratic polynomials. When the T -palindromic polynomial is real, then we derive the backward error of a real number considered as an approximate eigenvalue of the matrix po...

Structured Eigenvalue Backward Errors of Matrix Pencils and Polynomials with Hermitian and Related Structures

We derive a formula for the backward error of a complex number λ when considered as an approximate eigenvalue of a Hermitian matrix pencil or polynomial with respect to Hermitian perturbations. The same are also obtained for approximate eigenvalues of matrix pencils and polynomials with related structures like skew-Hermitian, ∗-even and ∗-odd. Numerical experiments suggest that in many cases th...

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...

Zero assignment of matrix pencils by additive structured transformations

γ-Iteration for Descriptor Systems Using Structured Matrix Pencils

The optimal infinite-horizon output (or measurement) feedback H∞ control problem is one of the central tasks in robust control, see, e.g., [12, 13, 22, 28, 30]. For standard state space systems, where the dynamics of the system are modelled by a linear constant coefficient ordinary differential equation, the analysis of this problem is well studied and numerical methods have been developed and ...