Dwell-time stability conditions for infinite dimensional impulsive systems

2021/06/21 by Sergey Dashkovskiy, Dashkovskiy, Sergey, В. И. Слынько +1
Engineering · Computer Science · Mathematics · #Stability and Controllability of Differential Equations #Nonlinear Dynamics and Pattern Formation #Numerical methods for differential equations

paper · pdf · doi:10.48550/arxiv.2106.11224

Abstract

We consider nonlinear impulsive systems on Banach spaces subjected to disturbances and look for dwell-time conditions guaranteeing the 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 use 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 systems.

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