Converse Lyapunov theorems for nonautonomous discrete-time systems |
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| Authors: | Zeng Zhijun |
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| Affiliation: | (1) Institute of Systems Science, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100080, P. R. China |
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| Abstract: | This paper presents converse Lyapunov theorems for exponential stability of nonautonomous discrete-time systems with disturbances and free of disturbances, respectively. It is shown that Lyapunov functions exist for discrete-time systems if the systems are exponentially stable. Moreover, in the periodic case, we explicitly construct a Lyapunov function for systems with disturbances. Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 61, Optimal Control, 2008. |
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