Journal
NONLINEAR ANALYSIS-HYBRID SYSTEMS
Volume 46, Issue -, Pages -Publisher
ELSEVIER SCI LTD
DOI: 10.1016/j.nahs.2022.101248
Keywords
Impulsivesystems; Input-to-statestability; Lyapunovmethod; Hybriddelayedimpulses; Indefinitederivative
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Funding
- National Natural Science Foundation of China [62173215]
- Major Basic Research Program of the Natural Science Foundation of Shandong Province in China [ZR2021ZD04, ZR2020ZD24]
- Support Plan for Outstanding Youth Innovation Team in Shandong Higher Education Institutions, PR China [2019KJI008]
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This paper investigates the input-to-state stability (ISS) and integral-input-to-state stability (iISS) of nonlinear impulsive systems with hybrid delayed impulses, and obtains some sufficient conditions ensuring ISS and iISS while fully considering the hybrid effects of delayed impulses.
This paper investigates input-to-state stability (ISS) and integral-input-to-state stability (iISS) of nonlinear impulsive systems with hybrid delayed impulses. Based on Lyapunov method, some sufficient conditions ensuring ISS and iISS of impulsive systems are obtained, where the time derivative of Lyapunov function is indefinite, and the hybrid effects of delayed impulses are also fully considered. It is shown that the impulsive system is ISS provided that the combined action of time delay existing in impulses, continuous dynamic, and the cumulative strength of hybrid impulses satisfies some conditions, even if the hybrid delayed impulses play a destabilizing effect on ISS. Examples and their simulations are presented to illustrate the applicability of the proposed results.
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