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

Abstract

In this paper, a global 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 novel parameter estimator and state observer design methodology together with combined standard backstepping and small-gain approach. Our design has three distinct features. Firstly, the parameter estimator and state observer does not follow the classical certainty-equivalence principle. Second, the design treats in a unified way unknown parameters and unmeasured states. Third, the technique by combining backstepping technique and small-gain theorem ensures robustness with respect to dynamic uncertainties. Finally, a numerical example is given to show that the proposed method can be applied to more general systems which do not satisfy the cascading upper diagonal dominance (CUDD) conditions developed in recent papers.