L∞-stability of nonlinear time-delay systems

By using Lyapunov-Razumikhin functional analysis, it is discussed for the L-infinity bounded input-bounded output stability criterion for a class of nonlinear systems with nonlinear finite time-delay. Under the conditions of the zero beings the uniformly asymptotically stable point of unforced systems and of the state equations and the output terms not being larger than some class K functions, this paper gives the L-infinity bounded input-bounded output stability criterion. This criterion is easy to test and determine.