Robust stabilization of uncertain delayed systems: application to model-following systems

In this paper, we present the theoretical development to stabilize a class of uncertain time-delay system and its application to model-following systems. The system under consideration is described in state space model containing state delay, uncertain parameters and disturbance. The main idea is to reduce the state of system into an equivalent one, by employing generalized transformation, which is easier to analyze its behavior and stability. Then, the min-max approach is employed to find the stabilizing control law. After that, a class of model-following system is introduced for controlling the error between the model and process. With the extended theorem, the suitable control law that guarantees model tracking is derived. Finally, two numerical simulations are illustrated to show the algorithm for applying the proposed theorems and the effectiveness of the designed control law in stabilizing the controlled systems.