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

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.