TY - GEN
T1 - Global Stability and Asymptotic Gain Imply Input-to-State Stability for State-Dependent Switched Systems
AU - Liu, Shenyu
AU - Liberzon, Daniel
N1 - Funding Information:
the NSF grant CMMI-1662708 and the AFOSR grant FA9550-17-1-0236.
Funding Information:
S. Liu and D. Liberzon are with the Coordinated Science Laboratory, University of Illinois at Urbana-Champaign, U.S.A. This work was supported by the NSF grant CMMI-1662708 and the AFOSR grant FA9550-17-1-0236.
Publisher Copyright:
© 2018 IEEE.
PY - 2018/7/2
Y1 - 2018/7/2
N2 - In this paper we study several stability properties for state-dependent switched systems. We examine the gap between global asymptotic stability and uniform global asymptotic stability, and illustrate it with an example. Several regularity assumptions are proposed in order to obtain the equivalence between these two stability properties. Based on this equivalence, we are able to show that global stability and asymptotic gain imply input-to-state stability for state-dependent switched systems, which is the main result of the paper. The proof consists of a bypass via an auxiliary system which takes in a bounded disturbance, and showing that this system is uniformly globally asymptotically stable.
AB - In this paper we study several stability properties for state-dependent switched systems. We examine the gap between global asymptotic stability and uniform global asymptotic stability, and illustrate it with an example. Several regularity assumptions are proposed in order to obtain the equivalence between these two stability properties. Based on this equivalence, we are able to show that global stability and asymptotic gain imply input-to-state stability for state-dependent switched systems, which is the main result of the paper. The proof consists of a bypass via an auxiliary system which takes in a bounded disturbance, and showing that this system is uniformly globally asymptotically stable.
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U2 - 10.1109/CDC.2018.8619364
DO - 10.1109/CDC.2018.8619364
M3 - Conference contribution
AN - SCOPUS:85062172556
T3 - Proceedings of the IEEE Conference on Decision and Control
SP - 2360
EP - 2365
BT - 2018 IEEE Conference on Decision and Control, CDC 2018
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 57th IEEE Conference on Decision and Control, CDC 2018
Y2 - 17 December 2018 through 19 December 2018
ER -