Observer based tracking control design for a Single-Link Robot Arm system with time varying delays in the presence of external disturbances

This paper considers the problem of tracking control for a single-link robot based on homogeneity. At first, by using lie derivatives, the system is written in normal form. Then, by creating error vector, the error based state space is created. Next, it is assumed that except first state, other states are not measurable, so an observer is proposed. Then by a step-by-step method, an output feedback control law to global stabilization of error state space is constructed and by a suitable Lyapunov-Krasovskii functional it is proven that the states converge to zero. The convergence of the error vector to zero means that the states are converging to the desired signal, which is the concept of tracking.