Semi-global robust stabilisation of disturbed nonlinear systems with state-dependent uncertainties: a DOBC approach

Abstract

The robust stabilisation for a general class of disturbed nonlinear systems subject to state-dependent uncertainties is addressed in this paper. Different from most existing results, the lumped uncertainty, including external disturbances and model uncertainties, is relaxed to be bounded by some nonlinear functions rather than constants in this paper. Based upon the classical design procedure of disturbance observer-based control (DOBC), a new continuous saturation-based dynamic controller is proposed to estimate the lumped uncertainty. By the delicate design of several compact sets, the qualitative robust stability of the closed-loop system is guaranteed in the sense that all the signals of the closed-loop system can converge to an arbitrarily small compact set in a finite time. Furthermore, when the external disturbances are constants, the semi-global asymptotic stability can also be guaranteed by the proposed controller. Finally, the relationship between system uncertainties and observer gain is shown by a numerical simulation example.

Keywords:

• Uncertainty estimation
• qualitative robust stability
• uncertain nonlinear systems
• semi-global stabilisation

Data availability statement

The data that support the findings of this study are available from the corresponding author, T. Li, upon reasonable request.

Additional information

Funding

This work was supported by grants from the Natural Science Foundation of China [grant numbers 62103194, 61903192], the Jiangsu provincial colleges of Natural Science General Program [grant number 21KJB120007], and Basic scientific research business expenses of Central Universities [grant number NT2021011].