Stability analysis of nonlinear systems with delayed impulses: a generalised average dwell-time scheme. (English) Zbl 07885493
Summary: 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.
MSC:
| 93D25 | Input-output approaches in control theory |
| 93C10 | Nonlinear systems in control theory |
| 93C27 | Impulsive control/observation systems |
| 93C43 | Delay control/observation systems |
Keywords:
generalised average dwell-time condition; impulsive nonlinear systems; delayed impulse; input-to-state stability; uniform stabilityReferences:
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