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

作者：Dashkovskiy, Sergey; Kosmykov, Michael; Mironchenko, Andrii; Naujok, Lars^*

来源：Nonlinear Analysis: Hybrid Systems , 2012, 6(3): 899-915.

DOI：10.1016/j.nahs.2012.02.001

• Impulsive systems
• Large-scale systems
• Lyapunov methods
• Input-to-state stability
• Time delays

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 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.

• 出版日期2012-8