Lyapunov characterizations on input-to-state stability of nonlinear systems with infinite delays

Xu，Xiang1,2; Liu，Lu1; Feng，Gang1

2022-12-01

10.1016/j.automatica.2022.110585

AUTOMATICA   Impact Factor & Quartile

0005-1098

1873-2836

This paper addresses Lyapunov characterizations on input-to-state stability (ISS) of time-varying nonlinear systems with infinite delays. With novel ISS definitions in the case of nonlinear systems with infinite delays, we present several results on their ISS Lyapunov characterizations in the form of both ISS Lyapunov theorems and converse ISS Lyapunov theorems. It is shown that an infinite-delayed system is (locally) ISS if it has a (local) ISS Lyapunov functional, and conversely, there exists a (local) ISS Lyapunov functional if it is (locally) ISS. To prove the converse ISS Lyapunov theorems, we establish a key technical lemma bridging ISS/LISS and robust asymptotic stability of systems with infinite delays and two converse Lyapunov theorems concerning robust asymptotic stability of systems with infinite delays. Two distinctive advantages of this work are that a large class of infinite dimensional spaces are allowed and the results are established based on a more general Lipschitz condition, i.e., the right hand side Lipschitz (RS-L) condition. An example is provided for illustration of the obtained results.

(Local) input-to-state stability Infinite delays Lyapunov characterizations Nonlinear systems

SCI ; EI

English

Others

Research Grants Council, University Grants Committee[CityU-11201120];Research Grants Council, University Grants Committee[CityU-11213518];

Automation & Control Systems ; Engineering

Automation & Control Systems ; Engineering, Electrical & Electronic

WOS:000862953600012

PERGAMON-ELSEVIER SCIENCE LTD

20223712727502

Asymptotic stability ; Lyapunov functions ; Lyapunov methods

Mathematics:921 ; Systems Science:961

ENGINEERING

2-s2.0-85137641412

Scopus

1.Department of Biomedical Engineering,City University of Hong Kong,Kowloon,Hong Kong
2.Department of Electronic and Electrical Engineering,Southern University of Science and Technology,Shenzhen,Guangdong Province,China

Xu，Xiang,Liu，Lu,Feng，Gang. Lyapunov characterizations on input-to-state stability of nonlinear systems with infinite delays[J]. AUTOMATICA,2022,146.

Xu，Xiang,Liu，Lu,&Feng，Gang.(2022).Lyapunov characterizations on input-to-state stability of nonlinear systems with infinite delays.AUTOMATICA,146.

Xu，Xiang,et al."Lyapunov characterizations on input-to-state stability of nonlinear systems with infinite delays".AUTOMATICA 146(2022).