Stability of linear systems with sawtooth input delay and predictor-based controller

In this paper, the stability of linear systems with sawtooth input delay widely existing in networked systems and predictor-based controller is considered. Under the assumption that there exists an instant where the input delay is zero, a necessary and sufficient condition is obtained to guarantee the exponential stability of the closed-loop system, that is, the closed-loop system is stable if and only if the matrix A+BK is Hurwitz. Two simulation examples are given to confirm the validity of the obtained results.