On Higher-Order Truncated Predictor Feedback for Linear Systems with Input Delay

This paper is concerned with the problem of stabilizing a linear system with input delay. Motivated by the first-order truncated predictor feedback (TPF) approach recently developed by the authors, a general higher-order TPF controller that contains higher-order terms of the nominal feedback gains is proposed. It is shown that this higher-order TPF can also globally and semi-globally stabilize the concerned time-delay systems in the absence and in the presence of input saturation, respectively. Safe implementation via numerical approximation of this higher-order TPF is also established. However, in spite of the fact that the higher-order TPF utilizes more information of the state, numerical examples have demonstrated that the first-order TPF outperforms the higher-order TPF, indicating that the intuition of higher-order approximation leading to better results is incorrect in this case.