Static State Feedback Controller Design for the Differentially Flat Systems via Minimum Projection Method

Abstract

We propose a “static” C^∞ differentiable control Lyapunov function (CLF) design method for differentially flat systems by dynamic extension and minimum projection method. For differentially flat systems, “dynamic” CLF with dynamic compensators are designed. Our proposed “static” CLF is obtained by the reduction of the “dynamic” CLF. Then we design a static state feedback controller with the obtained static CLF. Finally we show an example to show that our proposed static CLF based controller can stabilizes the origin of the system.