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

Abstract

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.

Keywords:

• Bounded control
• global stabilisation
• nonlinear feedback
• oscillator system
• state-dependent saturation functions

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported in part by the National Natural Science Foundation of China under grant numbers 61903102, 61773140 and 61773387, and by the Fundamental Research Funds for the Central Universities under the Grant No. HIT.BRET. 2021008.