Model reference stabilization approach for unstable first order linear systems with large time delay

In this paper, an approach of stabilization and control based on model reference scheme is proposed and analyzed for a class of unstable first order linear systems with time delay. This approach of design controller improved the performances of conventional Smith predictor compensator considerably, by incorporating an additional component of control law to generate a suitable input plant that satisfies the model reference behavior. The controller parameters are designed under assumptions of asymptotic stability and model matching conditions. Specifically, a control law is designed to ensure tracking error convergence and to reduce the instability region. Therefore, it's important to note that the method does not use the exact knowledge of the plant parameters and can guarantee an asymptotic stability with unknown bounded parameters system. Finally, a numerical example is presented to show applicability and performances of the proposed approach.