Input-to-state stability of switched systems with time delays

Zhong Ping Jiang; Yuandan Lin; Yuan Wang

doi:10.1007/978-3-319-18072-4_11

Input-to-state stability of switched systems with time delays

Zhong Ping Jiang, Yuandan Lin, Yuan Wang

Electrical and Computer Engineering

Research output: Chapter in Book/Report/Conference proceeding › Chapter

Abstract

This chapter deals with the input-to-state stability of switched nonlinear systems with time delays. The proposed results demonstrate a connection between small-gain arguments in the context of input-to-state stability and the traditional Lyapunov-Razumikhin method for switched systems. By using the notion of average dwell time, it is shown that a switching among ISS systems with compatible Lyapunov-Razumikhin functions will not destroy the stability property if the switching is not too fast on average. Particularly, it is shown that the existence of a common Razumikhin function is sufficient to guarantee input-to-state stability for time-delayed systems under arbitrary switching.

Original language	English (US)
Title of host publication	Recent Results on Nonlinear Delay Control Systems
Subtitle of host publication	In honor of Miroslav Krstic
Publisher	Springer International Publishing
Pages	225-241
Number of pages	17
Volume	4
ISBN (Electronic)	9783319180724
ISBN (Print)	9783319180717
DOIs	https://doi.org/10.1007/978-3-319-18072-4_11
State	Published - Jul 15 2015

ASJC Scopus subject areas

General Engineering
General Computer Science

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10.1007/978-3-319-18072-4_11

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abstract = "This chapter deals with the input-to-state stability of switched nonlinear systems with time delays. The proposed results demonstrate a connection between small-gain arguments in the context of input-to-state stability and the traditional Lyapunov-Razumikhin method for switched systems. By using the notion of average dwell time, it is shown that a switching among ISS systems with compatible Lyapunov-Razumikhin functions will not destroy the stability property if the switching is not too fast on average. Particularly, it is shown that the existence of a common Razumikhin function is sufficient to guarantee input-to-state stability for time-delayed systems under arbitrary switching.",

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PY - 2015/7/15

Y1 - 2015/7/15

N2 - This chapter deals with the input-to-state stability of switched nonlinear systems with time delays. The proposed results demonstrate a connection between small-gain arguments in the context of input-to-state stability and the traditional Lyapunov-Razumikhin method for switched systems. By using the notion of average dwell time, it is shown that a switching among ISS systems with compatible Lyapunov-Razumikhin functions will not destroy the stability property if the switching is not too fast on average. Particularly, it is shown that the existence of a common Razumikhin function is sufficient to guarantee input-to-state stability for time-delayed systems under arbitrary switching.

AB - This chapter deals with the input-to-state stability of switched nonlinear systems with time delays. The proposed results demonstrate a connection between small-gain arguments in the context of input-to-state stability and the traditional Lyapunov-Razumikhin method for switched systems. By using the notion of average dwell time, it is shown that a switching among ISS systems with compatible Lyapunov-Razumikhin functions will not destroy the stability property if the switching is not too fast on average. Particularly, it is shown that the existence of a common Razumikhin function is sufficient to guarantee input-to-state stability for time-delayed systems under arbitrary switching.

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Input-to-state stability of switched systems with time delays

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