Global stabilization of the double integrator system with saturation and delay in the input

This paper is concerned with the problem of global stabilizing a double integrator system subject to actuator saturation and delay in the input. Two solutions to the problem are proposed by using linear state feedback which are parameterized in a single scalar γ. The first solution is delay-dependent in the sense that the delay information is directly used in the feedback design. The second solution is delay-independent as the delay information is not directly used in the feedback. Ranges of the value of the free parameter γ are established within which the closed-loop system is globally asymptotically stable. A numerical example is used to illustrate the effectiveness of the proposed approach.