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## Linear perturbation theory for structured matrix pencils arising in control theory

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Author(s) : Shreemayee Bora , Volker Mehrmann

Preprint series of the Institute of Mathematics, Technische Universität Berlin
Preprint 16-2004

MSC 2000

93B36 $^\infty$-control
65F15 Eigenvalues, eigenvectors

Abstract :
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 $H_\infty$ control and linear quadratic control for continuous and discrete time systems.

Keywords : $H_\infty$ control, linear-quadratic control, Hamiltonian matrix, continuous-time control, discrete-time control, skew-Hamiltonian/Hamiltonian pencil, Hermitian/Hermitian pencil