Stability of the Zero Solution of Impulsive Differential Equations by the Lyapunov Second Method

Abstract

AbstractThe paper is concerned with the stability of the zero solution of the impulsive system dxdt=ft,x,t≠θixΔx|t=θi(x)=Jix,i∈N=(1,2,…), where Δx|t=θ≔x(θ+)−x(θ), x(θ+)=limt→θ+x(t). The Lyapunov second method is used as a tool in obtaining the criteria for stability, asymptotic stability, and instability of the trivial solution