State-feedback implementation of cascade compensators
For a general dynamical system \(\Sigma\) we say that a cascade compensator \({\bar \Sigma}\) can be implemented with state feedback if there exists a state feedback law F such that the input-output behavior of the closed- loop system \(\Sigma_ F\) is the same as the input-output behavior of the cascade connection of \(\Sigma\) with \({\bar \Sigma}\). The purpose of this paper is to characterize those cascade compensators for \(\Sigma\) which can be implemented with state feedback. For a controllable, observable linear system \(\Sigma\) with transfer matrix \(T_{\Sigma}\) it is shown hat an invertible linear cascade compensator with transfer matrix \(\bar T\) can be implemented with state feedback if and only if the McMillan degree of \(T_{\Sigma}\) is equal to the McMillan degree of \([T_{\Sigma},\bar T^{-1}]^ t\).
scientific article; zbMATH DE number 3999744