Some results on the properties of discrete-time LTI state-space systems

This work brings forward several interesting facts about system properties of LTI discrete-time systems like output controllability, state controllability and state observability, trackability and input and state observability. Particularly, the work brings about the inter-relationships between these properties while taking a state-space formulation based approach to come up with simple facts that are backed up by proofs using preliminary linear algebra.