Delay Independent Truncated Predictor Feedback for Continuous-Time Linear Systems

Abstract

The truncated predictor feedback design simplifies the predictor feedback design by discarding the distributed delay term. The implementation of the remaining static feedback term of the predictor feedback law requires the exact knowledge of the input delay. The truncated predictor state feedback law for continuous-time linear systems with a constant delay is such an example. The exact value of the delay appears in the exponential factor eAτ of the truncated predictor feedback law. Moreover, the determination of the value of the feedback parameter of the truncated predictor feedback law requires, although not the exact value of the delay, an upper bound of the delay to be known. This requirement of the information of the delay, which explicitly or implicitly appears in the truncated predictor feedback law, suggests that the truncated predictor feedback law is delay-dependent. The delay-dependency of the truncated predictor feedback law also manifests itself in the observer based feedback design. To construct an observer whose state asymptotically approaches the state of the open loop system, the dynamics of the observer generally contains the delayed input. This implies that the exact value of the delay is also required in the construction of the observer used in the observer based truncated predictor feedback law.