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

Yu Kang, Niankun Zhang and Guoyong Chen

Applied Mathematics and Computation, 2023, vol. 436, issue C

Abstract: 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 functions 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 functions (MSLFs) method involving mode-dependent average impulsive interval (MDAII) approach, we consider two special cases in which switching and impulses are completely asynchronous and synchronous respectively, and successfully establish the relation of impulse 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 various 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 stability conditions of the considered systems without switches are gained directly, which enshrouds the existing results.

Keywords: Impulsive systems; Switched positive systems; Mode-dependent average impulsive interval (search for similar items in EconPapers)
Date: 2023
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Citations: View citations in EconPapers (4)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:436:y:2023:i:c:s0096300322005896

DOI: 10.1016/j.amc.2022.127515

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