Global stability by output feedback control for a class of nondifferentiable uncertain nonlinear systems

Abstract

In this paper, we study the problem of global stabilization by output feedback for a class of nondifferentiable uncertain nonlinear systems of a planar system whose Jacobian linearization is uncontrollable and unobservable, and might not exist. Hence, the stabilization problem cannot be solved by any linear feedback control approach even locally. A truly nonlinear control design must be used. To solve this difficult problem, we propose a C° non-Lipschitz control law and an observer based on the concept of homogeneity and domination design approaches. Our control design does not base the separation principle. Both control law and observer are simultaneously constructed in a step-by-step design manner.