Control for Time-Varying Delay Systems by Integrating Semi-Discretization and Hysteresis-Based Switching

In this paper, we develop an innovative control method for linear systems with time-varying delay by integrating the semi-discretization method and the hysteresis-based switching algorithm. The semi-discretization method is adopted to design an optimal controller for each fixed time-delay and form a candidate controller family. The switching algorithm acts as the principal law for switching among various controllers according to the instantaneous value of the time-delay. A theoretical proof is presented regarding the stability of the switching time-delay system. It is shown that the most significant factors that affect the system stability are the size of the candidate controller family, the value of the switching coefficient, and the changing rate of the time-delay. Two case studies are presented to show the effectiveness of the proposed method.