On improving transient performance in global control of multiple integrators system by bounded feedback

The global stabilization problem for multiple integrators systems by bounded control is considered. Two classes of nonlinear feedback laws are proposed. The first one consisting of nested saturation functions is a modification and generalization of that in [A.R. Teel, Global stabilization and restricted tracking for multiple integrators with bounded controls, Systems & Control Letters 18 (3) (1992) 165-171] and the other one consists of parallel connections of saturation functions. Both these two types of nonlinear feedback laws need only over(n, ̃) (over(n, ̃) = frac(n, 2) if n is even and over(n, ̃) = frac(n + 1, 2) if n is odd, where n is the length of the multiple integrators) saturation elements. Furthermore, the poles of the closed-loop system can be placed on any location of the left real axis when none of the saturation elements in the control laws is saturated. Both of them exhibit simpler structure, can significantly improve the transient performance of the closed-loop system, and are very superior to the other existing methods. Simulation of a fourth-order system is used to illustrate the effectiveness of the proposed methods.