Backstepping Design of Robust Controllers for a Class of Nonlinear Systems

Abstract

We present a backstepping procedure for designing non-dynamic feedback compensators for a class of uncertain nonlinear systems. We assume knowledge of nonlinear growth bounds on the system uncertainties, and we require that these bounds satisfy a strict feedback condition (a condition much less restrictive than the matching condition). We develop two design procedures, one for systems whose uncertainties vanish at an equilibrium point (in which case we achieve global uniform asymptotic stability) and one for systems with more general types of uncertainties (in which case we achieve global uniform ultimate boundedness).