State-feedback implementation of cascade compensators

For a general dynamical system Σ and cascade compensation conditions are developed for the existence of a state-feedback law F which when applied to Σ causes the result-ing closed-loop system ΣF to exhibit the same input-output behavior as the cascade connection of Σ with . For a controllable, observable linear system Σ with transfer matrix TΣ, it is shown that an invertible linear cascade compensator with transfer matrix . can be implemented with state feedback if and only if the McMillan Degree of TΣ equals the McMillan Degree of .