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.