Stability analysis of nonlinear systems with delayed impulses: a generalised average dwell-time scheme (Q6577136)

This paper deals with the input-to-state stability and uniform stability of nonlinear systems with delayed impulses, the delays between two consecutive impulsive instants being flexible. The paper introduces concepts of generalised average impulsive delay and generalised reverse average impulsive delay, more useful in applications, and illustrates the effects caused by delays. Further, sufficient conditions for input-to-state stability and uniform stability are first derived based on a general Lyapunov function and with certain proposed generalised techniques. The obtained results show that double effects due to delayed impulses are present and can be observed intuitively. Finally, two examples illustrate the presented results.