Similarity invariants for a class of linear controlled systems
type: Item
instance of: scholarly article
title: Similarity invariants for a class of linear controlled systems
zbMATH Open document ID: 1027.93008
DOI: 10.1023/A:1017989420691
author: Yanyan Li
published in: Differential Equations
publication date: 2003-05-25T00:00:00Z
review text: The matrices \(A\), \(B\) and \(C\) defining the linear control system have complex coefficients. Making a linear transformation of the state coordinates we get an algebraic action of the group \(\text{GL}_n(\mathbb{C})\) on the space of linear systems, which is called a similarity action. A theory of invariants leads to classification problems for linear systems. In the present paper the authors suggest a simple proof of the fact that for systems with one-dimensional inputs and outputs the algebra of polynomial \(G\)-invariants of linear systems is free and the basis of invariants consists of algebraically independent elements.
Mathematics Subject Classification ID: 93B10
Mathematics Subject Classification ID: 93C05
Mathematics Subject Classification ID: 93B25
Mathematics Subject Classification ID: 93B17
zbMATH DE Number: 1915978
zbMATH Keywords: free algebra of invariants
zbMATH Keywords: linear transformation
zbMATH Keywords: similarity action
zbMATH Keywords: invariants
reviewed by: Constantin Vârsan
MaRDI profile type: Publication
full work available at URL: a:1017989420691
OpenAlex ID: W130128078
description: scientific article; zbMATH DE number 1915978