Stabilisation and tracking controllers for a class of nonlinear systems with unmatched nonvanishing perturbations

Abstract

This article is concerned with the systematic design of robust stabilising and tracking controllers for a certain class of nonlinear systems suffering from unmatched and nonvanishing disturbances and nonlinearities, the combined action of which is referred to as ‘perturbations’. The proposed composite state feedback controllers combine a linear and a nonlinear component, the design of which is based on simple and mature control design methodologies (pole placement and Lyapunov redesign). The novel design of the nonlinear component guarantees the Uniform Ultimate Boundedness (UUB) of the error between the plant and a model representing the ideal behaviour. It is also shown how the stabilisation result can be generalised for the case where matched uncertainties and nonlinearities are also present in the plant. The efficacy of the proposed methodologies is demonstrated via numerical examples.

Keywords:

• Control theory
• robust control
• nonlinear control

Disclosure statement

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

Additional information

Funding

The author acknowledges financial support from the ASPETE Special Account for Research (ELKE).

Notes on contributors

Leonidas Dritsas

Leonidas Dritsas is currently an Associate Professor at the School of Pedagogical and Technological Education, Greece (ASPETE). He holds a Diploma Degree and a Ph.D. degree in Electrical & Computer Engineering, University of Patras, (1985, 2009, respectively) and a M.Sc. in Electrical & Computer Engineering, Drexel University (1987). His research interests are in Robust, Nonlinear and Networked Control Systems.