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

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