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.

(2023). Do 0-GAS-Guaranteeing Impulse Sequences Preserve ISS or iISS Properties? Not Always . Retrieved from https://hdl.handle.net/10446/299790

Do 0-GAS-Guaranteeing Impulse Sequences Preserve ISS or iISS Properties? Not Always

Russo, Antonio;
2023-01-01

Abstract

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.
2023
Russo, Antonio; Liu, Shenyu
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10446/299790
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