Global stabilization and restricted tracking with bounded feedback for multiple oscillator systems

This paper is concerned with the problems of global stabilization and restricted tracking for a multiple oscillator system by bounded feedback. A nonlinear feedback law consisting of nested saturation functions is proposed to achieve global stabilization. To improve the transient performance of the closed-loop system, the parameters in this feedback law can be tuned to assign the poles of the closed-loop system when none of the saturation elements in the control law is in effect. The proposed feedback law is also shown to achieve restricted tracking. Simulation results are given to show the effectiveness of the proposed feedback law.