Improved Razumikhin-Type Theorem for Input-To-State Stability of Nonlinear Time-Delay Systems

Author

Chongyang Ning ; Yong He ; Min Wu ; Jinhua She

Author_Institution

Sch. of Inf. Sci. & Eng., Central South Univ., Changsha, China

Volume

59

Issue

7

fYear

2014

fDate

Jul-14

Firstpage

1983

Lastpage

1988

Abstract

This note describes a Lyapunov-Razumikhin function with an indefinite derivative that can be used to determine the input-to-state stability (ISS) of a nonlinear time-delay system. First, an extended comparison principle for estimating the solution of a differential inequality with an upper bound that is not (semi)negative definite is presented. Then, that principle and a Lyapunov-Razumikhin function with an indefinite derivative are employed to derive an ISS criterion. Finally, two examples show the effectiveness of our method and its superiority over others.

Keywords

delay systems; nonlinear control systems; stability; Lyapunov-Razumikhin function; Razumikhin-type theorem; differential inequality; indefinite derivative; input-to-state stability; nonlinear time-delay systems; Asymptotic stability; Educational institutions; Estimation; Stability criteria; Thermal stability; Upper bound; Indefinite derivative; Lyapunov–Razumikhin function; input-to-state stability (ISS); nonlinear systems;

fLanguage

English

Journal_Title

Automatic Control, IEEE Transactions on

Publisher

ieee

ISSN

0018-9286

Type

jour

DOI

10.1109/TAC.2013.2297183

Filename

6698360