For many physical systems, there are inevitable uncertainties such as parameters variation, unknown disturbance, and unmodeled dynamics, etc. Designing a stabilizing control for these systems is called robust control. There are two methods. One is the Lyapunov function based method, the other is the differential geometric methods of feedback linearization. But these methods basically must be satisfied with the so-called matching conditions. The key component in the matching conditions is the uncertainties are in the range space of input matrix of the nominal system.
This paper is proposed to Backstepping control using time delay estimation for the systems whether are satisfied with the matching conditions or not satisfied with the matching conditions. Time delay estimation is used to estimate the uncertainties and Backstepping is used to design the control input guaranteeing the stability. We applied the proposed method to a motor system, a rigid-link flexible-joint robot and the overhead crane system.
