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

Huijuan Li; Junxia Wang

doi:10.3934/dcdsb.2019192

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2020, Volume 25, Issue 3: 841-857. Doi: 10.3934/dcdsb.2019192

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

Huijuan Li^, and
Junxia Wang

1.
School of Mathematics and Physics, China University of Geosciences (Wuhan), 430074, Wuhan, China

^* Corresponding author: Huijuan Li
^* Corresponding author: Huijuan Li

Received: October 31, 2018

Revised: February 28, 2019

Early access: September 2019

Published: March 2020

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

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Abstract

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.

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

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