TY - GEN
T1 - A Lyapunov Krasovskii Functional for Input-to-State Stability of Infinite-Delayed Systems
AU - Xu, Xiang
AU - Feng, Gang
PY - 2021/7
Y1 - 2021/7
N2 - This paper mainly addresses input-to-state stability (ISS) of nonautonomous nonlinear systems with infinite delays. We provide a novel definition for ISS of infinite-delayed systems, which can be seen as an extension of the existing ISS definition. A Lyapunov Krasovskii functional is proposed for verifying ISS of infinite-delayed systems. Applying the ISS Lyapunov functional method, a link between ISS of an infinite-delayed system and the exponential stability of its corresponding zero-input system is established. It is shown that a nonlinear system with infinite delays is ISS if its corresponding zero-input system is globally exponentially stable, provided that some Lipschitz and/or Lipschitz-like conditions are satisfied. Two illustrative examples are provided to show the effectiveness of our results.
AB - This paper mainly addresses input-to-state stability (ISS) of nonautonomous nonlinear systems with infinite delays. We provide a novel definition for ISS of infinite-delayed systems, which can be seen as an extension of the existing ISS definition. A Lyapunov Krasovskii functional is proposed for verifying ISS of infinite-delayed systems. Applying the ISS Lyapunov functional method, a link between ISS of an infinite-delayed system and the exponential stability of its corresponding zero-input system is established. It is shown that a nonlinear system with infinite delays is ISS if its corresponding zero-input system is globally exponentially stable, provided that some Lipschitz and/or Lipschitz-like conditions are satisfied. Two illustrative examples are provided to show the effectiveness of our results.
KW - Infinite delays
KW - input-to-state stability
KW - Lyapunov Krasovskii functional
KW - nonlinear systems
UR - http://www.scopus.com/inward/record.url?scp=85117270205&partnerID=8YFLogxK
UR - https://www.scopus.com/record/pubmetrics.uri?eid=2-s2.0-85117270205&origin=recordpage
U2 - 10.23919/CCC52363.2021.9550609
DO - 10.23919/CCC52363.2021.9550609
M3 - 32_Refereed conference paper (with host publication)
SN - 9781665411950
T3 - Chinese Control Conference, CCC
SP - 391
EP - 396
BT - Proceedings of the 40th Chinese Control Conference, CCC 2021
A2 - Peng, Chen
A2 - Sun, Jian
PB - IEEE Computer Society
T2 - 40th Chinese Control Conference (CCC 2021)
Y2 - 26 July 2021 through 28 July 2021
ER -