On state-space representations of general discrete-time dynamical systems

TL;DR

This paper proves that all deterministic, non-autonomous, discrete-time, causal, time-invariant systems can be represented using state-space models and explores the conditions for their minimality.

Contribution

It establishes the existence of state-space representations for a broad class of discrete-time systems and discusses their minimality conditions.

Findings

Every such system has a state-space representation.

Conditions for minimality are discussed.

The results unify understanding of system representations.

Abstract

In this paper we establish that every (deterministic) non-autonomous, discrete-time, causal, time invariant system has a state-space representation, and discuss its minimality.