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Input-to-state stability of impulsive systems with delayed impulse effects
Xiaodi Li,Haitao Zhu,Peng Li,Li Sun
Keywords:Impulsive systems; Delayed impulses; Input-to-state stability (ISS); Integral input-to-state stability (iISS); Lyapunov method.
      The goal of this paper is to study properties of input-to-state stability (ISS) and integral input-to-state stability (iISS) of impulsive systems with delayed impulses, and a set of Lyapunov-based sufficient conditions ensur- ing ISS/iISS properties are obtained. Those conditions reveal the effects of delayed impulses on ISS/iISS and establish the relationship between impulsive frequency and the time delay existing in impulses. When the continuous dynamics of the system are stabilizing, the ISS property can be retained under the impulse scheme even if there exist destabilizing impulses. Conversely, when the impulse dynamics are stabilizing, but the continuous dynamics are not, the ISS property can be obtained if the interval between impulses are not overly long. Two illustrative examples are presented, with their numerical simulations, to demonstrate the effectiveness of the main results.