fast finite-time stability and stabilization of nonlinear impulsive systems

Abstract The issue of fast finite-time stability and stabilization design for a class of nonlinear impulsive systems is discussed in this paper. In previous finite-time control designs for impulsive systems, the convergence rate of these control strategies is even less rapid than the exponential convergence rate when the initial state is distant from the origin. To overcome this problem, a nonlinear impulse system is obtained by mathematical modeling of the mechanical buffer. The fast finite-time stability criterion is established for this system, and the upper bound of the settling-time is evaluated. In addition, combining Lyapunov functions theory and impulsive control, we design a controller for impulsive dynamical systems to satisfy fast finite-time stability. Finally, two simulation examples are given,in which the first example demonstrates the superiority of the fast finite-time stability criterion for nonlinear impulsive systems by comparing it with traditional finite-time stability, and the second example verifies the effectiveness of the presented controller.