Discontinuous exponential stabilization of chained form systems

A transformation is proposed for single chained form systems. This transformation puts chained form systems in a form close to the Brunovsky linear canonical form and can be utilized to derive an almost stabilizing feedback. This feedback is then extended in order to treat the singularity that arises for some initial conditions in the previous approach. The so obtained feedback is static and discontinuous and globally exponentially stabilizes chained form systems. This feedback law has the advantageous property of being bounded for bounded states and converging to zero along the trajectories of the closed-loop system. This work is straightforwardly extendable to multi-input chained systems.