Input-to-state stability of nonlinear impulsive systems
Abstract
We prove that impulsive systems, which possess an ISS Lyapunov function, are ISS for time sequences satisfying the fixed dwell-time condition. If an ISS Lyapunov function is the exponential one, we provide a stronger result, which guarantees uniform ISS of the whole system over sequences satisfying the generalized average dwell-time condition. Then we prove two small-gain theorems that provide a construction of an ISS Lyapunov function for an interconnection of impulsive systems, if the ISS-Lyapunov functions for subsystems are known. The construction of local ISS Lyapunov functions via linearization method is provided. Relations between small-gain and dwell-time conditions as well as between different types of dwell-time conditions are also investigated. Although our results are novel already in the context of finite-dimensional systems, we prove them for systems based on differential equations in Banach spaces that makes obtained results considerably more general.
Keywords
Cite
@article{arxiv.1212.5481,
title = {Input-to-state stability of nonlinear impulsive systems},
author = {Sergey Dashkovskiy and Andrii Mironchenko},
journal= {arXiv preprint arXiv:1212.5481},
year = {2012}
}