A novel nested non-linear feedback law for global stabilisation of linear systems with bounded controls

Abstract

A novel nested non-linear feedback law for global stabilisation of a chain of integrators with bounded controls is proposed, which can be directly applied on the system without state transformation as soon as a so-called -stable polynomial is constructed. Then the so-called state-dependent saturation function is introduced into this novel nested non-linear feedback law to replace the standard saturation function, which can significantly improve the convergence performance of the closed-loop system. The results are then extended to a wider class of linear system that can be globally stabilised by bounded controls. Two numerical examples show the effectiveness of the proposed approach.