A Short Note on Output Controllability

TL;DR

This paper introduces a Hautus-type criterion for output controllability in linear time-invariant systems, extending classical results and unifying the concept with state controllability.

Contribution

It provides a Hautus-type characterization of output controllability for LTI systems, complementing existing Kalman-type criteria and covering the case when the output matrix is the identity.

Findings

Hautus-type criterion for output controllability derived

Criterion reduces to state controllability when output matrix is identity

Extends classical control theory results to output controllability

Abstract

In this paper we consider output controllability for linear time-invariant systems. In a recent paper by Danhane, Loh{\'e}ac and Jungers it has been pointed out that although output controllability is a classical notion in control theory, only a Kalman-type characterization was available in the literature. In their work that authors consider time-varying linear systems. In this short note we provide a Hautus-type characterization of output controllability for time-invariant linear systems which is more comprehensive and reduces to state controllability in case the output matrix is the identity matrix.