Stability analysis of nonlinear systems with delayed impulses: a generalised average dwell-time scheme

Abstract

This paper studies the input-to-state stability (ISS) and uniform stability for impulsive nonlinear systems with delayed impulses, where delays are flexible between two consecutive impulsive instants. Illustrating effects caused by delays, concepts of generalised average impulsive delay and generalised reverse average impulsive delay are introduced, and more applicable in practice. Moreover, sufficient conditions for stability properties are formulated with destabilising and stabilising impulses through a general candidate ISS-Lyapunov function and the generalised conditions. It is shown that the double effects of delays in impulses (i.e. stabilising an initial unstable system, or contrarily, destabilising an initial stable system) coincide with the existing results using the exponential candidate ISS-Lyapunov function. Finally, two examples are provided to demonstrate our developed techniques.

Keywords:

• Generalised average dwell-time condition
• impulsive nonlinear systems
• delayed impulse
• input-to-state stability
• uniform stability

Disclosure statement

No potential conflict of interest was reported by the author(s).

Data availability statement

The data that support the findings of this study are available from the corresponding author upon reasonable request.

Additional information

Funding

This work was supported in part by the Natural Science Foundation of China under Grant 61973092 and by the Guangdong Basic and Applied Basic Research Foundation under Grant 2019A1515012104.