Null controllability of neutral system with infinite delays

Sufficient conditions are developed for the null controllability of neutral control systems with infinite delays when the values of the control lie in an mm-dimensional unit cube. Conditions are placed on the perturbation function which guarantee that if the uncontrolled system is uniformly asymptotically stable and the control system satisfies a full rank condition, so that K(λ)ξ(exp(−λh))≠0K(λ)ξ(exp(−λh))≠0, for every complex λλ, where K(λ)K(λ) is an n×nn×n polynomial matrix in λλ constructed from the coefficient matrices of the control system and ξ(exp(−λh))ξ(exp(−λh)) is the transpose of [1,exp(−λh),⋯,exp(−(n−1)λh)], then the control system is null controllable with constraint.