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

Wim Michiels (1) , K. Green , 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 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. © 2005 IEEE.

Mots clés: Computational methods; Delay control systems; Differential equations; Perturbation techniques; Analytic matrix function; Delay differential equations; Pseudospectra; Matrix algebra

Domaines: Automatique / Robotique

Wim Michiels, K. Green, T. Wagenknecht, Silviu-Iulian Niculescu. Pseudospectra for analytic matrix functions and application to time-delay systems. 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05, Dec 2005, Seville, Spain. pp.4336-4341, ⟨10.1109/CDC.2005.1582844⟩. ⟨hal-02294290⟩