Finite-time stability of inelastic ball bouncing between two rigidly connected harmonic limiters

This paper formulates the bouncing ball system in gravitational field, where a ball bounces between two rigidly connected harmonic limiters, by the impulsive differential equations with state constraints. By an extended Lyapunov-like stability theory for impulsive systems, we obtain the sufficient conditions guaranteeing the ball will stay on the lower limiter after a finite time but maybe an infinite number of impacts. The upper bound of the finite time is also estimated by theoretical analysis. Some numerical simulations are given to verify the theoretical validity.