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Converse Lyapunov theorems for nonautonomous discrete-time systems

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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.

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Authors and Affiliations

  1. Institute of Systems Science, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100080, P. R. China

    Zhijun Zeng

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  1. Zhijun Zeng
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Correspondence to Zhijun Zeng.

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Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 61, Optimal Control, 2008.

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Zhijun, Z. Converse Lyapunov theorems for nonautonomous discrete-time systems. J Math Sci 161, 337–343 (2009). https://doi.org/10.1007/s10958-009-9557-1

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