On minimal LPV state-space representations in innovation form: an algebraic characterization

TL;DR

This paper defines minimal LPV state-space representations in innovation form, provides algebraic conditions for minimality, and proposes an algorithm to transform any LPV model into a minimal innovation form.

Contribution

It introduces a formal definition of minimal LPV innovation form and offers an algebraic characterization and transformation algorithm.

Findings

Algebraic conditions for minimal LPV innovation form

A systematic algorithm for minimal realization transformation

Enhanced understanding of LPV state-space minimality

Abstract

In this paper we will propose a definition of the concept of minimal state-space representations in innovation form for LPV. We also present algebraic conditions for a stochastic LPV state-space representation to be minimal in forward innovation form and discuss an algorithm for transforming any stochastic LPV state-space representation to a minimal one in innovation form.