Journal of Mathematical Sciences

, Volume 161, Issue 2, pp 337–343 | Cite as

Converse Lyapunov theorems for nonautonomous discrete-time systems



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.


Lyapunov Function Exponential Stability Model Predictive Control Exponential Convergence Periodic Case 


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Copyright information

© Springer Science+Business Media, Inc. 2009

Authors and Affiliations

  1. 1.Institute of Systems Science, Academy of Mathematics and Systems ScienceChinese Academy of SciencesBeijingP. R. China

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