Stabilization of some linear systems with both state and input delays

This paper studies the stabilization problem for some linear systems with both state and input time-varying delays. Three classes of systems are considered. The first class of systems consists of a chain of integrators with constant delays in both the state and the input. The second and the third classes of systems have respectively multiple point and distributed time-varying delays in both the state and the control. The parametric Lyapunov equation based approach is utilized to design stabilization controllers for these three classes of systems. Moreover, it is shown that the designed controllers can stabilize the systems semi-globally in the presence of input saturation. Two numerical examples are worked out to illustrate the effectiveness of the proposed approaches.