Reachability of discrete time ARMA representations

Abstract

Abstract A new formula for the solution of discrete time auto-regressive moving average (ARMA) representations is provided. Then, the concept of reachability (also known as controllability from the origin) is examined by showcasing the reachable subspace of the system and the consistent inputs that drive the system to a desired state, taking into account the admissible initial conditions. The theory is illustrated by an example and the study of the special cases of ARMA representations, i.e. state space systems, descriptor systems and causal systems.