Practical Finite-Time Stability of Nonlinear Systems With Delayed Impulsive Control

The article investigates the practical finite-time stability (PFTS) issue of continuous-time nonlinear systems with disturbance. Some extended Lyapunov results for semi-global/global PFTS, including attraction domain and settling time estimation are obtained based on a relaxed Lyapunov condition. Especially, for systems with stabilizing delayed impulses, a new scheme of delayed impulsive control involving a finite number of impulses is proposed to realize semi-global and/or global PFTS, where the minimum number of impulses can be explicitly designed in terms of initial states. Optimal delayed impulsive control design is provided in different situations to yield the minimum settling time estimation. Several numerical examples illustrate the validity of the obtained results finally.

Automated summary

The article investigates the issue of practical finite-time stability (PFTS) in continuous-time nonlinear systems with disturbance. Extended Lyapunov results for semi-global/global PFTS are obtained, including attraction domain and settling time estimation, based on a relaxed Lyapunov condition. Specifically, a new scheme of delayed impulsive control involving a finite number of impulses is proposed for systems with stabilizing delayed impulses, achieving semi-global and/or global PFTS with explicitly designed minimum number of impulses in terms of initial states. Optimal delayed impulsive control design is provided to yield minimum settling time estimation in different situations. Several numerical examples are presented to validate the obtained results.