Some Results on the Properties of Discrete-Time LTI State-Space Systems

Abstract

This work brings forward several interesting facts about system properties of linear time-invariant 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.