Sampled-data periodic predictor feedback for linear systems with input delay

In this paper we propose sampled-data periodic predictor feedback controllers for linear systems with input delay. For any size of input delay and any prescribed sampling period, an explicit sampled-data periodic predictor feedback controller is constructed and shown to be able to stabilize the given delay system. Such a controller utilizes only the state information at the latest sampling instant and the control inputs at some past sampling instants. Under the condition that the open-loop system is not exponentially unstable (but maybe polynomially unstable), a truncated version of the sampled-data periodic predictor feedback controller is also proposed, which is a memoryless controller that needs only the state at the latest sampling instant. Stability of the closed-loop system under the truncated sampled-data periodic predictor feedback controller is proven. Two numerical examples are given to illustrate the effectiveness of the proposed designs.