Bounded control of multiple oscillators system by using state-dependent saturation functions

This paper is concerned with the global stabilisation problem of multiple oscillators system with bounded controls by constructing state-dependent saturation functions. First, two types of planar systems subject to input additive disturbances are respectively stabilised by bounded feedbacks whose formulas involve state-dependent saturation function. Next, these results are used to stabilise multiple oscillators system of arbitrary length with bounded control based on a special canonical form. Explicit conditions are provided to guarantee the stability of the closed-loop system. Compared with the existing results, the proposed controllers contain the so-called state-dependent saturation functions and thus can improve the control performance significantly. Moreover, the corresponding results for the discrete-time case are also established. Two numerical examples are given to show the effectiveness and superiority of the proposed approaches.