Contraction Theory Approach to Disturbance Observer Based Filtered Backstepping Design

Various practical applications use filtered backstepping technique, which follows the same procedure as backstepping design but uses high gain filters to circumvent the analytical computation of derivatives. As a result, there exists a time-scale separation between the system dynamics and the fast filter dynamics. This paper proposes a new contraction theory-based technique to design a high gain disturbance observer-based filtered backstepping controller and to quantify the convergence bounds in terms of design parameters. The quantification of the bounds explicitly shows the dependency of the closed-loop performance on various parameters, which in turn provide more ways to tune the performance apart from reducing the magnitude of filter parameter. Unlike the existing results, the proposed approach relaxes the conservative restriction, required on the filter parameter to achieve a satisfactory closed loop performance. The efficacy of the proposed method is verified through simulation examples.