Uniform asymptotic stability of a discontinuous predator-prey model under control via non-autonomous systems theory

The present paper deals with uniform stability for non-autonomous impulsive systems. We consider a non-autonomous system with impulses in its abstract form and we present conditions to obtain uniform stability, uniform asymptotic stability and global uniform asymptotic stability using Lyapunov functions. Using the results from the abstract theory we present sufficient conditions for a controlled predator-prey model under impulse conditions to be globally uniformly asymptotically stable.