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

Discrete and Continuous Dynamical Systems

Volumn 9, Issue 5, 2003, Pages 1223-1241

  Pötzsche, Christian ^a   Siegmund, Stefan ^b   Wirth, Fabian ^c  

^a UNIVERSITY OF AUGSBURG   (Germany)

^b UNIVERSITY OF CALIFORNIA   (United States)

^c UNIVERSITY OF BREMEN   (Germany)

Author keywords

Exponential Stability; Linear Dynamic Equation; Time Scale

Indexed keywords

EID: 0038446654     PISSN: 10780947     EISSN: None     Source Type: Journal    
DOI: 10.3934/dcds.2003.9.1223     Document Type: Article

References (14)

1. Agarwal, R.P. (1992): Difference Equations and Inequalities, Marcel Dekker Inc., New York
2. Aulbach, B.; Hilger, S. (1990): Linear dynamic processes with inhomogeneous time scale, Nonlinear Dynamics and Quantum Dynamical Systems (G.A. Leonov, V. Reitmann, W. Timmermann; eds.), 9-20. Mathematical Research 59, Akademie-Verlag, Berlin
3. Bohner, M.; Peterson, A. (2001): Dynamic Equations on Time Scales, Birkhäuser, Boston
4. Cesari, L. (1971): Asymptotic Behavior and Stability Problems in Ordinary Differential Equations. Springer-Verlag, Berlin 3rd edition.
5. Daleckii, J.L.; Krein, M.G. (1974): Stability of Solutions of Differential Equations in Banach Spaces, Translations of Mathematical Monographs 43. American Mathematical Society, Providence, Rhode Island
6. Gard, T.; Hoffacker, J. (to appear): Asymptotic behavior of natural growth on time scales, Dynamic Systems and Applications
7. Hahn, W. (1967): Stability of Motion, Grundlehren der mathematischen Wissenschaften, 138, Springer-Verlag, New York
8. Hilger, S. (1988): Ein Maßkettenkalkül mit Anwendung auf Zentrumsmannigfaltigkeiten, Ph.D. thesis, Universität Würzburg, Germany
9. Hilger, S. (1990): Analysis on measure chains - A unified approach to continuous and discrete calculus, Results in Mathematics 18, 18-56.
10. Hilger, S.; Kloeden, P.E. (1994): Comparative time grainyness and asymptotic stability of dynamical systems, Autom. Remote Control 55, 1293-1298.
11. Keller, S. (1999): Asymptotisches Verhalten invarianter Faserbündel bei Diskretisierung und Mittelwertbildung im Rahmen der Analysis auf Zeitskalen, Ph.D. thesis, Augsburger Mathematische Schriften 36, Wißner Verlag, Augsburg
12. Pötzsche, C. (2002): Langsame Faserbündel dynamischer Gleichungen auf Maßketten, Ph.D. thesis, Logos Verlag, Berlin
13. Stewart, G.W.; Sun, J. (1990): Matrix perturbation theory, Computer Science and Scientific Computing. Academic Press, Boston
14. Walters, P. (1982): An Introduction to Ergodic Theory, Springer-Verlag, New York