Stability of interconnected impulsive systems with and without time delays, using Lyapunov methods

By Sergey N. Dashkovskiy, Michael Kosmykov, Andrii Mironchenko, Lars Naujok. 2010

156 citations recorded by the source corpus.

Abstract In this paper, we consider the input-to-state stability (ISS) of impulsive control systems with and without time delays. We prove that, if the time-delay system possesses an exponential Lyapunov–Razumikhin function or an exponential Lyapunov–Krasovskii functional, then the system is uniformly ISS provided that the average dwell-time condition is satisfied. Then, we consider large-scale networks of impulsive systems with and without time delays and prove that the whole network is uniformly ISS under the small-gain and the average dwell-time condition. Moreover, these theorems provide us with tools to construct a Lyapunov function (for time-delay systems, a Lyapunov–Krasovskii functional or a Lyapunov–Razumikhin function) and the corresponding gains of the whole system, using the Lyapunov functions of the subsystems and the internal gains, which are linear and satisfy the small-gain condition. We illustrate the application of the main results on examples.

View Paper: https://www.semanticscholar.org/paper/baab7461364c62163d6e020f47e4fb549436021e

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Citations in the corpus

• Stability of nonlinear differential systems with state-dependent delayed impulses (2016, background): “In addition, ifwe exclude explicit dependence on time t , then Corollary 1 becomes a special case of Dashkovskiy et al. (2012).”