A Contraction Theory Approach for Analysis of Performance Recovery in Dynamic Surface Control

Dynamic surface control (DSC) method uses high gain filters to avoid the ”explosion of complexity” issue inherent in backstepping based controller designs. As a result, the closed loop system and filter dynamics possess time scale separation between them. This paper attempts to design a novel disturbance observer based dynamic surface controller using contraction framework. In doing so the steady state error bounds are obtained in terms of design parameters which are exploited to tune the closed loop system performance. The results not only show that DSC technique recover the performance of a backstepping controller for a small range of filter parameter but also derive the maximum bound for it. Furthermore the stability bounds are also derived in the presence of disturbances and convergence of trajectories to a small penultimate bound is proved. The convergence results are shown to hold for less conservative choice of filter parameter and observer gain. The effectiveness of the proposed controller is verified through simulation example.