TY - JOUR
T1 - Exponential stability of nonlinear time-delay systems with delayed impulse effects
AU - Chen, Wu-Hua
AU - Zheng, Wei Xing
PY - 2011
Y1 - 2011
N2 - The problem of exponential stability for nonlinear time-delay systems with delayed impulses is addressed in this paper. Lyapunov-based sufficient conditions for exponential stability are derived, respectively, for two kinds of delayed impulses (i.e., destabilizing delayed impulses and stabilizing delayed impulses). It is shown that if a nonlinear impulsive time-delay system without impulse input delays is exponentially stable, then under some conditions, its stability is robust with respect to small impulse input delays. Moreover, it is also shown that for a stable nonlinear impulsive time-delay system, if the magnitude of the delayed impulses is sufficiently small, then under some conditions, the delayed impulses do not destroy the stability irrespective of the sizes of the impulse input delays. The efficiency of the proposed results is illustrated by three numerical examples.
AB - The problem of exponential stability for nonlinear time-delay systems with delayed impulses is addressed in this paper. Lyapunov-based sufficient conditions for exponential stability are derived, respectively, for two kinds of delayed impulses (i.e., destabilizing delayed impulses and stabilizing delayed impulses). It is shown that if a nonlinear impulsive time-delay system without impulse input delays is exponentially stable, then under some conditions, its stability is robust with respect to small impulse input delays. Moreover, it is also shown that for a stable nonlinear impulsive time-delay system, if the magnitude of the delayed impulses is sufficiently small, then under some conditions, the delayed impulses do not destroy the stability irrespective of the sizes of the impulse input delays. The efficiency of the proposed results is illustrated by three numerical examples.
UR - http://handle.uws.edu.au:8081/1959.7/553089
U2 - 10.1016/j.automatica.2011.02.031
DO - 10.1016/j.automatica.2011.02.031
M3 - Article
SN - 0005-1098
VL - 47
SP - 1075
EP - 1083
JO - Automatica
JF - Automatica
IS - 5
ER -