Dwell-time stability conditions for infinite dimensional impulsive systems

We consider nonlinear impulsive systems on Banach spaces subjected to disturbances and look for dwell-time conditions guaranteeing the ISS property. In contrary to many existing results our conditions cover the case where both continuous and discrete dynamics can be unstable simultaneously. Lyapunov type methods are used for this purpose. The effectiveness of our approach is illustrated on a rather nontrivial example, which is feedback connection of an ODE and a PDE system.(c) 2022 Elsevier Ltd. All rights reserved.

Automated summary

This paper considers nonlinear impulsive systems on Banach spaces under disturbances and aims to find dwell-time conditions that guarantee the ISS property. Unlike many existing results, our conditions cover the case where both continuous and discrete dynamics can be unstable simultaneously. Lyapunov type methods are used for this purpose. The effectiveness of the approach is illustrated with a rather nontrivial example, which involves the feedback connection of an ODE and a PDE system.