TY - GEN
T1 - Do 0-GAS-Guaranteeing Impulse Sequences Preserve ISS or iISS Properties? Not Always
AU - Russo, Antonio
AU - Liu, Shenyu
N1 - Publisher Copyright:
© 2023 IEEE.
PY - 2023
Y1 - 2023
N2 - Based on the recent work on determination of classes of impulse/switching signals, uniformly over which a switched or impulsive system is input-to-state stable (ISS) or integral input-to-state stable (iISS), it is conjectured that for a switched system with all ISS or iISS subsystems, as long as the impulse/switching signal makes the system 0-input globally asymptotically stable (0-GAS), then it also ensures ISS and iISS, respectively. This work disproves this conjecture by showing examples where the impulse sequence amplifies the input, causing 0-GAS impulsive system to lose the ISS or iISS properties. As a compensation, we provide sufficient conditions on the impulse sequences which guarantee ISS or iISS. It turns out that these conditions are strictly stronger than those ensuring 0-GAS; the differences between them are in fact necessary conditions for the impulsive system to have the asymptotic gain (AG) property or uniformly bounded energy bounded state (UBEBS) property.
AB - Based on the recent work on determination of classes of impulse/switching signals, uniformly over which a switched or impulsive system is input-to-state stable (ISS) or integral input-to-state stable (iISS), it is conjectured that for a switched system with all ISS or iISS subsystems, as long as the impulse/switching signal makes the system 0-input globally asymptotically stable (0-GAS), then it also ensures ISS and iISS, respectively. This work disproves this conjecture by showing examples where the impulse sequence amplifies the input, causing 0-GAS impulsive system to lose the ISS or iISS properties. As a compensation, we provide sufficient conditions on the impulse sequences which guarantee ISS or iISS. It turns out that these conditions are strictly stronger than those ensuring 0-GAS; the differences between them are in fact necessary conditions for the impulsive system to have the asymptotic gain (AG) property or uniformly bounded energy bounded state (UBEBS) property.
UR - http://www.scopus.com/inward/record.url?scp=85184829877&partnerID=8YFLogxK
U2 - 10.1109/CDC49753.2023.10383527
DO - 10.1109/CDC49753.2023.10383527
M3 - Conference contribution
AN - SCOPUS:85184829877
T3 - Proceedings of the IEEE Conference on Decision and Control
SP - 7655
EP - 7660
BT - 2023 62nd IEEE Conference on Decision and Control, CDC 2023
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 62nd IEEE Conference on Decision and Control, CDC 2023
Y2 - 13 December 2023 through 15 December 2023
ER -