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Simple High-Order Sliding Mode Controller Design Subject to Uncertainties Bounded by Positive Functions

A new global HOSM controller, that constructed in a simple relay polynomial form, is proposed for a general class of uncertain nonlinear systems with arbitrary known relative degree n. The conventional constant upper bounds assumption imposed on the uncertainties is extended to time-varying positive functions. Different from the existing HOSM methods, the proposed controller consists of two parts, one of which is discontinuous and used to suppress the uncertainties, the other of which is continuous and provides the convergence of HOSMs to zero. The Lyapunov analysis shows the finite-time stability of the closed-loop HOSM system even in the presence of uncertainties bounded by positive functions. Simulation example is given to show the effectiveness of the proposed method.