Constructions of ISS-Lyapunov functions for interconnected impulsive systems

Abstract

In this paper we provide two small-gain theorems for impulsive systems. The first of them provides a construction of an ISS-Lyapunov function for interconnections of impulsive systems if ISS-Lyapunov functions for subsystems are given and a small-gain condition holds. If, in addition, these given ISSLyapunov functions are exponential then the second theorem provides a construction of an exponential ISS-Lyapunov function for the interconnection if the gains are power functions.

Local Input-to-State Stability of Production Networks

“…If there exists a LISS or ISS Lyapunov function for the subsystem then it has the LISS or ISS property respectively. Furthermore, if the LISS Lyapunov gains or ISS Lyapunov gains satisfy the small gain condition, then the whole system of the form (5) is LISS or ISS respectively (see [2], [3] or [4]). …”