Global Stabilization of the Multiple Integrators System by Delayed and Bounded Controls

This note is concerned with global stabilization of multiple integrators by delayed and bounded controllers. Three types of new nonlinear control laws are proposed based on some special canonical forms and explicit conditions are proposed to guarantee the global stability of the closed-loop systems. Differently from the existing canonical forms, the new special canonical forms used in this note contain not only time delay in the input but also time delays in its state, which are essential in the recursive design since they lead to natural cancellation. Moreover, some free parameters are introduced into these controllers. These advantages can help to improve the transient performance of the closed-loop system significantly. Numerical simulations for the fourth order integrators illustrate that the proposed new controllers can indeed outperform the existing one.