Boundedness and Stability in Nonlinear Discrete Systems With Nonlinear Perturbation

摘要

We consider the nonlinear Volterra discrete system with nonlinear peturbation x(n+1) = A(n)x(n) + Σ from s=0 to n of B(n,s)f(s,x(s)) + g(n,x(n)). Our goal is to use Lyapunov functionals to obtain conditions that guarantee all solutions of the above Volterra equation are bounded and derive conditions that ensure asymptotic stability and exponential stability, in the case x = 0 is a solution.