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**Exponential stability of nonlinear time-delay systems with delayed impulse effects.**
*(English)*
Zbl 1233.93080

Summary: 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.

### MSC:

93D20 | Asymptotic stability in control theory |

93C10 | Nonlinear systems in control theory |

93D09 | Robust stability |

93C15 | Control/observation systems governed by ordinary differential equations |

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\textit{W.-H. Chen} and \textit{W. X. Zheng}, Automatica 47, No. 5, 1075--1083 (2011; Zbl 1233.93080)

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### References:

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