Analysis of a set of nonlinear dynamics trajectories: Stability of difference equations

For a set of difference equations generated by discretization of the set of differential equations with Hukuhara derivative a principle of comparison with matrix Lyapunov function is specified and sufficient stability conditions of certain type are established. The analysis is carried out in terms o...

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Bibliographic Details
Published in:Journal of mathematical analysis and applications 2015-01, Vol.421 (1), p.105-117
Main Authors: Aleksandrov, A.Yu, Martynyuk, A.A., Platonov, A.V.
Format: Article
Language:English
Subjects:
Asymptotic stability
Comparison method
Lyapunov function
Set of difference systems
Switched systems
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Summary:For a set of difference equations generated by discretization of the set of differential equations with Hukuhara derivative a principle of comparison with matrix Lyapunov function is specified and sufficient stability conditions of certain type are established. The analysis is carried out in terms of a matrix Lyapunov function of special structure. For an essentially nonlinear multiconnected switched difference system, conditions are obtained providing the asymptotic stability of its zero solution for any switching law. An example is presented to demonstrate efficiency of the proposed approaches.
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2014.07.003