Truncated Predictor Feedback for Continuous-Time Linear Systems

Abstract

A difficulty arises in the implementation of a predictor feedback law with the distributed delay term in it. To overcome this implementation difficulty, Lin and Fang (IEEE Trans. Autom. Control 52(6), 998–1013 (2007)) proposed to truncate the distributed delay term from the predictor feedback law, implementing only the remaining static state feedback term. This leads to a truncated predictor feedback (TPF) law, which can be readily implemented. In this chapter, we introduce the intuition, expression, and construction of the TPF law and its output feedback counterpart. In particular, the construction of the feedback gain matrix of the truncated predictor feedback law is first carried out by using an eigenstructure assignment based low gain feedback design technique. An alternative design is then presented by using the Lyapunov equation based low gain design technique. Stabilization of linear systems with input delay by the TPF is established under both the eigenstructure assignment based TPF and the Lyapunov equation based TPF.