Global stabilization of linear systems via bounded controls

This paper is concerned with global stabilization of linear systems by bounded controls. Two types of nonlinear control laws with one made of cascade connections of saturation functions and the other one consisting of nested connections of saturation functions are firstly proposed for multiple integrators system. The possible ranges for the controllers’ parameters are extended with respect to existing results. Simultaneously, the so-called state-dependent saturation functions are introduced into these two types of control laws to replace the standard saturation functions which can improve the transient performance of the closed-loop system significantly. The results are then extended to a class of linear systems that can be globally stabilized by bounded controls. An illustrative example is presented to show the effectiveness and advantages of the proposed approaches.