Robust stabilization of a class of non - minimum - phase nonlinear systems in a generalized output feedback canonical form

Abstract

In this paper, a globally robust stabilizer for a class of uncertain non-minimum-phase nonlinear systems in generalized output feedback canonical form is designed. The system contains unknown parameters multiplied by output-dependent nonlinearities and output-dependent nonlinearities enter such a system both additively and multiplicatively. The proposed method relies on a recently developed novel parameter estimator and state observer design methodology together with a combination of backstepping and small-gain approach. Our design has three distinct features. First, the parameter estimator and state observer do not necessarily follow the classical certainty-equivalent principle any more. Second, the design treats unknown parameters and unmeasured states in a unified way. Third, the technique by combining standard backstepping and small-gain theorem ensures robustness with respect to dynamic uncertainties. Finally, two numerical examples are given to show that the proposed method is effective, and that it can be applied to more general systems that do not satisfy the cascading upper diagonal dominance conditions developed in recent papers, respectively.