Global exponential stability of impulsive switched positive nonlinear systems with mode-dependent impulses

The global exponential stability for a type of continuous-time impulsive switched positive nonlinear systems (ISPNSs) with average dwell time (ADT) switching and mode-dependent impulsive effects is explored in this research . Where we consider a type of nonnegative impulses, which do not need to be in step with the switching behaviors in the constructed systems. The main challenge of this study comes from the estimation of Lyapunov func-tions within any time interval under the coupling effect of asynchronous switches and state jumps. To solve this difficulty, based on the multiple max-separable Lyapunov func-tions (MSLFs) method involving mode-dependent average impulsive interval (MDAII) ap-proach, we consider two special cases in which switching and impulses are completely asynchronous and synchronous respectively, and successfully establish the relation of im-pulse strength, system modes, ADT and MDAII. Subsequently, several stability criteria are presented for ISPNSs with unstable and/or stable modes. In particular, the impact of var-ious sorts of impulses on stability are also analysed in depth. Then, the obtained results are applied to the ISPNSs with synchronous impulses and switching. Moreover, the sta-bility conditions of the considered systems without switches are gained directly, which enshrouds the existing results.(c) 2022 Elsevier Inc. All rights reserved.

Automated summary

This research explores the global exponential stability of a type of continuous-time impulsive switched positive nonlinear systems (ISPNSs) with average dwell time switching and mode-dependent impulsive effects. By introducing the multiple max-separable Lyapunov functions method, the relation between impulse strength, system modes, average dwell time, and mode-dependent average impulsive interval is successfully established, and several stability conditions are presented.