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 and bounded (time-varying) delay in the actuator. A new class of feedback laws based on pole-assignment low gain design is proposed 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 is presented. By using properties of this class of new feedback laws and the properties of some transcendental equations, exact zeros distribution of the closed-loop system is discussed. As a result, necessary and sufficient condition is given to guarantee the stability of the closed-loop system. All the conditions given in the paper are independent of the low gain parameter and are convenient to use in practice. Numerical example is given to illustrate the effectiveness of the proposed approach.