Stabilization of a class of linear systems with input delay and the zero distribution of their characteristic equations

This paper is concerned with stabilization of linear systems with arbitrarily large but bounded time-varying delay in the input. A pole assignment based low gain feedback design is adopted to solve the problem. Both delay-dependent and delay-independent results are presented and a series of sufficient conditions for guaranteeing the stability of the closed-loop system are established. By using properties of this class of low gain feedback laws and the properties of certain transcendental equations, distribution of the zeros of the closed-loop characteristic equation is described. As a result, a necessary and sufficient condition is identified that guarantees the stability of the closed-loop system. A numerical example is given to illustrate the effectiveness of the proposed approach.