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September  2003, 9(5): 1223-1241. doi: 10.3934/dcds.2003.9.1223

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

Christian Pötzsche 1, , Stefan Siegmund 2, and  Fabian Wirth 3,

1. 

Institut für Mathematik, Universität Augsburg, 86135 Augsburg, Germany
2. 

Department of Mathematics, University of California at Berkeley, Berkeley, CA 94720, United States
3. 

Zentrum für Technomathematik, Universität Bremen, 28334 Bremen, Germany

Received  November 2002 Published  June 2003

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.
Keywords: Time scale, linear dynamic equation, exponential stability..
Mathematics Subject Classification: 34C11, 39A10, 37B55, 34D9.
Citation: Christian Pötzsche, Stefan Siegmund, Fabian Wirth. A spectral characterization of exponential stability for linear time-invariant systems on time scales. Discrete and Continuous Dynamical Systems, 2003, 9 (5) : 1223-1241. doi: 10.3934/dcds.2003.9.1223
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