A spectral characterization of exponential stability for linear time-invariant systems on time scales

Publikation: Beitrag in FachzeitschriftForschungsartikelBeigetragenBegutachtung

Beitragende

  • Christian Pötzsche - , Universität Augsburg (Autor:in)
  • Stefan Siegmund - , University of California at Berkeley (Autor:in)
  • Fabian Wirth - , Universität Bremen (Autor:in)

Abstract

We prove a necessary and sufficient condition for the exponential stability of time-invariant linear systems on time scales in terms of the eigenvalues of the system matrix. In particular, this unifies the corresponding characterizations for finite-dimensional differential and difference equations. To this end we use a representation formula for the transition matrix of Jordan reducible systems in the regressive case. Also we give conditions under which the obtained characterizations can be exactly calculated and explicitly calculate the region of stability for several examples.

Details

OriginalspracheEnglisch
Seiten (von - bis)1223-1241
Seitenumfang19
Fachzeitschrift Discrete and continuous dynamical systems
Jahrgang9
Ausgabenummer5
PublikationsstatusVeröffentlicht - Sept. 2003
Peer-Review-StatusJa
Extern publiziertJa

Externe IDs

ORCID /0000-0003-0967-6747/work/149795385

Schlagworte

Schlagwörter

  • Exponential Stability, Linear Dynamic Equation, Time Scale