A new control method and stability analysis of linear system with variable time-delay

This paper proposes an effective control method aimed at the linear system with time-varying delay. We address the problem by means of switching among a finite family of candidate controllers. Our control method is based on semi-discretization method and hysteresis-based switching algorithms, where the former is introduced to design the candidate controller under one fixed time delay and the latter acts as the principal law of the switching. We prove the stability of our switching delay system and conclude that three factors, the size of the candidate controller set, the value of the switching coefficient, the changing rate of the delay, affect the system´s stability, which can also be demonstrated by several groups of experiments. Simulation results show the correctness of our design.