Dynamic Extensions for Exact Backstepping Control of Systems in Pure Feedback Form

Abstract

The traditional backstepping design may struggle to asymptotically stabilize systems in pure feedback form, due to implicit equations. Approximation based designs only have a limited domain of validity and turn out sensitive to disturbances. We propose a new design that circumvents the necessity of solving implicit algebraic equations by introducing new state variables. Additional augmentations to the backstepping Lyapunov design lead to explicit expressions for the associated differential equations. The result is a dynamic state feedback, capable of asymptotically stabilizing the origin of a general class of nonlinear systems, based on just standard assumptions.