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Combining Methods of Lyapunov for Exponential Stability of Linear Dynamic Systems on Time Scales
Department of Mathematics, Vietnam Water Resource University, Hanoi, Vietnam
Department of Mathematics, Vietnam National University of Science, Hanoi, Vietnam
- 1 Department of Mathematics, Vietnam Water Resource University, Hanoi, Vietnam
- 2 Department of Mathematics, Vietnam National University of Science, Hanoi, Vietnam
Applied Mathematics·Volume 05 (2014)·Pages 3452–3459·Published 1 December 2014·DOI10.4236/am.2014.521323
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Abstract
Consider the linear dynamic equation on time scales (1) where , , is a rd-continuous function, T is a time scales. In this paper, we shall investigate some results for the exponential stability of the dynamic Equation (1) by combinating the first approximate method and the second method of Lyapunov.
KeywordsTime ScalesExponential StabilityLinear Dynamic Equation
- Hilger, S. (1990) Analysis on Measure Chains—A Unified Approach to Continuous and Discrete Calculus. Results in Mathematics, 18, 19-56. http://dx.doi.org/10.1007/BF03323153
- Bohner, M. and Peterson, A. (2001) Dynamic Equation on Time Scales: An Introduction with Applications. Birkhauser, Boston. http://dx.doi.org/10.1007/978-1-4612-0201-1
- Kaymakacalan, B., Lakshmikantham, V. and Sivasundaram, S. (1996) Dynamic Systems on Measure Chains. Kluwer, Dordrecht.
- Potzsche, C., Siegmund, S. and Wirth, F. (2003) A Spectral Characterization of Exponential Stability for Linear Time-Invariant Systems on Time Scales. Discrete and Continuous Dynamical Systems, 9, 1223-1241. http://dx.doi.org/10.3934/dcds.2003.9.1223
- Agarwal, R., Bohner, M., O’Regan, D. and Peterson, A. (2002) Dynamic Equation on Time Scales: A Survey. Journal of Computational and Applied Mathematics, 141, 1-26. http://dx.doi.org/10.1016/S0377-0427(01)00432-0
- Aulback, B. and Hilger, S. (1971) Linear Dynamic Processes with Inhomogeneous Time Scale. In: Nonlinear Dynamics and Quantum Dynamical Systems, 3rd Edition, Akademie-Verlag, Berlin, Mathematical Research Bd. 59.
- Akin-Bohner, E., Bohner, M. and Akin, F. (2005) Pachpatte Inequalities on Time Scales. Journal of Inequalities in Pure and Applied Mathematics, 6, 23.