Traditional backstepping approaches may struggle to asymptotically stabilize systems in pure feedback form, due to its inherent implicit equations. Approximation based designs only have a limited domain of validity and turn out sensitive to model uncertainty and 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.
Dr. Johann Reger received his diploma degree (Dipl.-Ing.) in Mechanical Engineering in 1999 and his doctorate (Dr.-Ing.) in Control Engineering in 2004, both from the University of Erlangen-Nuremberg in Germany. He has held several postdoc positions, among others, with the Mechatronics Department at CINVESTAV-IPN in Mexico-City, the EECS Control Laboratory at the University of Michigan in Ann Arbor, and the Control Systems Group at TU Berlin. Since 2008 he is a full professor and head of the Control Engineering Group at the Computer Science and Automation Faculty, TU Ilmenau, in Germany. There he also serves as vice-dean and director of the Institute for Automation and Systems Engineering. His current research foci are on adaptive and robust control, variable structure and sliding mode control, state and parameter estimation. Application areas include robotics, mechatronics, automotive, and water systems.