Truncated predictor feedback for linear systems with long time-varying input delays

In this paper we study the problem of stabilizing a linear system with a single long time-varying delay in the input. Under the assumption that the open-loop system is stabilizable and not exponentially unstable, a finite dimensional static time-varying linear state feedback controller is obtained by truncating the predictor based controller and by adopting the parametric Lyapunov equation based controller design approach. As long as the time-varying delay is exactly known and bounded, an 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 subject to either magnitude saturation or energy constraints. Numerical examples show the effectiveness of the proposed approach. (c) 2012 Elsevier Ltd. All rights reserved.