About Stability Radii

Paul Van Dooren

Universite Catholique de Louvain

November 2,



ABSTRACT: The basic stability radius problem can be defined as follows. Let A be a stable matrix with all its eigenvalues in the stability region S (typically the open left half plane or the open unit disc). The stability radius of A is the norm of smallest (complex) perturbation D that causes at least one eigenvalue of A+D to become unstable, i.e.

This problem is well studied by several authors and there exists an analytic formulation for rc as well as a quadratically convergent algorithm to compute it.

In this talk we discuss several variants and extensions of this standard problem to the generalized eigenvalue problem, to polynomial matrices, to the periodic eigenvalue problem and to structured matrices. We also talk about the use of different norms as well as structured perturbations and link this problem to the concept of pseudospectra.

This is ongoing work with Y. Genin, C. Lawrence, Y. Nesterov, C. Oara, J. Sreedhar, A. Tits and V. Vermaut.

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