Pseudospectra and stability radii for analytic matrix functions with application to time-delay systems

Wim Michiels (1) , K. Green (2) , T. Wagenknecht (2) , Silviu-Iulian Niculescu (3)

1 Department of Computer Science - K.U.Leuven
2 University of Bristol [Bristol]
3 Heudiasyc - Heuristique et Diagnostic des Systèmes Complexes [Compiègne]

Definitions for pseudospectra and stability radii of an analytic matrix function are given, where the structure of the function is exploited. Various perturbation measures are considered and computationally tractable formulae are derived. The results are applied to a class of retarded delay differential equations. Special properties of the pseudospectra of such equations are determined and illustrated. © 2006 Elsevier Inc. All rights reserved.

Mots clés: Delay equations; Pseudospectrum; Robustness; Stability

Domaines: Automatique / Robotique

Wim Michiels, K. Green, T. Wagenknecht, Silviu-Iulian Niculescu. Pseudospectra and stability radii for analytic matrix functions with application to time-delay systems. Linear Algebra and its Applications, 2006, 418 (1), pp.315-335. ⟨10.1016/j.laa.2006.02.036⟩. ⟨hal-02294073⟩