On obtaining the coefficients of the output transfer function from a state-space model and an output model of a linear constant coefficient system

A compact procedure for the calculation of the coefficients of the output transfer function of a system is presented. The coefficients of the plant characteristic polynomial are obtained as an explicit byproduct of this approach. Some additional insight into the consequence of the system´s state being unobservable by the output is gained. If the state is fully observable via the output, the characteristic polynomial of the system state transfer matrix is determined.