A note on the causality of singular linear discrete time systems

TL;DR

This paper investigates the causality properties of non-homogeneous linear singular discrete-time systems with constant matrix coefficients, focusing on the relationship between states, inputs, and outputs under sampled input changes.

Contribution

It provides new properties and conditions for causality in singular discrete-time systems with constant matrices, considering sampled input variations.

Findings

Causality conditions between state and inputs established.

Causality conditions between output and inputs analyzed.

Properties depend on system matrices and sampling assumptions.

Abstract

In this article we study the causality of non-homogeneous linear singular discrete time systems whose coefficients are square constant matrices. By assuming that the input vector changes only at equally space sampling instants we provide properties for causality between state and inputs and causality between output and inputs.