Stability criteria of linear systems with multiple input delays under truncated predictor feedback

Abstract

The model reduction technique as a feedback design approach for linear systems with input delays achieves finite spectrum assignment of the closed-loop system in a delay free form. The resulting predictor-type feedback law contains a distributed term that involves the convolution between the past input and the state transition matrix and hence causes difficulty in its implementation. For the purpose of easy implementation, the truncated predictor feedback (TPF) simplifies the predictor feedback by discarding the distributed term, and delay independent truncated predictor feedback further eliminates the delay-dependent exponential factor. In this paper, we consider the stabilization of a general linear system with multiple time-varying input delays by TPF or delay independent TPF. Stability criteria expressed in terms of input delays and the feedback parameter are derived through Lyapunov–Krasovskii stability analysis, and then numerically studied under both feedback laws.