Effect of delayed impulses on input-to-state stability of nonlinear systems

This paper studies the input-to-state stability (ISS) and integral input-to-state stability (iISS) of nonlinear systems with delayed impulses. By using Lyapunov method and the analysis technique proposed by Hespanha et al. (2005), some sufficient conditions ensuring ISS/iISS of the addressed systems are obtained. Those conditions establish the relationship between impulsive frequency and the time delay existing in impulses, and reveal the effect of delayed impulses on ISS/iISS. An example is provided to illustrate the efficiency of the obtained results.