Global Stabilization of Multiple Oscillator Systems by Delayed and Bounded Feedback

The problem of global stabilization for the multiple oscillator systems by bounded and delayed controls is considered. Based on a special canonical form of the considered system, a nonlinear control law consisting of nested saturation functions is proposed to achieve global stabilization. The new special canonical form used in this brief contains not only time delay in the input but also time delays in its state, which leads to natural cancellation and helps to not only provide explicit conditions guaranteeing the global stability of the closed-loop systems but also improves the transient performance of the closed-loop system significantly. The proposed feedback law is also adopted to achieve restricted tracking. A numerical simulation is given to illustrate the effectiveness of the proposed method.