Control design of linear systems with variable time-delay based on hysteresis-based switching algorithms and semi-discretization

We put forward a new control method combined with semi-discretization and the hysteresis-based switching algorithms for linear system with time-varying delay. Semi-discretization method proposes to discretize the time-delay and consider it to be a constant in a switching period, and treat the rest of the variables as continuous, so the system equation can be described by an ordinary differential equation. Using semi-discretization method, we can design an optimal controller for the system at a specific time. Obviously, optimal controllers vary at different time-delays. Since the time-delay varies with time going, we need to switch among different controllers in order to keep the system stable. As to how to switch, we introduce the hysteresis-based switching algorithm. Moreover, a series of simulation results have proved that this new method is able to give a fine performance in controlling such systems.