A truncated prediction approach to stabilization of linear systems with long time-varying input delay

This paper studies the problem of stabilizing a linear system with long time-varying delay in the input. Under the assumption that the open-loop system is not exponentially unstable and stabilizable, a finite dimensional static time-varying linear state feedback controller is obtained by truncating the prediction based controller and by adopting the parametric Lyapunov equation based low gain feedback. As long as the time-varying delay is exactly known and bounded, explicit condition is provided to guarantee the stability of the closed-loop system. It is also shown that the proposed controller achieves semi-global stabilization of the system if its actuator is also subject to saturation. Numerical examples show the effectiveness of the proposed approach.