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Input-to-state stability of continuous-time systems via finite-time Lyapunov functions

  • * Corresponding author: Huijuan Li

    * Corresponding author: Huijuan Li 

This work was partially supported by National Natural Science Foundation of China [NSFC11701533]

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  • In this paper, input-to-state stability (ISS) of continuous-time systems is analyzed via finite-time Lyapunov functions. ISS of a continuous-time system is first proved via finite-time robust Lyapunov functions for an introduced auxiliary system of the considered system. It is then obtained that the existence of a finite-time ISS Lyapunov function implies that the continuous-time system is ISS. The converse finite-time ISS Lyapunov theorem is proposed. Furthermore, we explore the properties of finite-time ISS Lyapunov functions for the continuous-time system on a bounded and compact set without a small neighborhood of the origin. The effectiveness of our results is illustrated by four examples.

    Mathematics Subject Classification: Primary: 37B25, 93D25; Secondary: 34D20.


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