A controllability test for general first-order representations
type: Item
instance of: scholarly article
title: A controllability test for general first-order representations
zbMATH Open document ID: 0874.93018
DOI: 10.1016/S0005-1098(96)00154-9
published in: Automatica
publication date: 1997-11-10T00:00:00Z
review text: The paper contains results on controllability for generalized linear finite-dimensional control systems with constant coefficients. Since the mathematical model presented in the paper is purely algebraic, both discrete and continuous systems can be considered. Using methods of linear algebra, the form of the generalized controllability matrix is given. Then, a necessary and sufficient rank condition for controllability is formulated and proved using different types of linear transformations in the state space. The space of reachable states is also defined using the concept of controllability matrix. Two simple illustrative numerical examples are also given. Moreover, the relationships to the existing results on controllability for generalized systems are discussed. Similar controllability problems for generalized systems can be found in the paper [\textit{J. C. Willems}, IEEE Trans. Autom. Control 36, No. 3, 259-294 (1991; Zbl 0737.93004)].
Mathematics Subject Classification ID: 93B05
Mathematics Subject Classification ID: 93C35
Mathematics Subject Classification ID: 93C05
zbMATH DE Number: 1008758
zbMATH Keywords: implicit systems
zbMATH Keywords: generalized linear control systems
zbMATH Keywords: controllability
zbMATH Keywords: controllability matrix
zbMATH Keywords: reachable states
author: Uwe Helmke
author: Joachim Rosenthal
author: Johannes M. Schumacher
reviewed by: Jerzy Klamka
MaRDI profile type: Publication
cites work: Implicit linear systems
cites work: Impulsive-smooth behavior in multimode systems. I: State-space and polynomial representations
cites work: Impulsive-smooth behavior in multimode systems. II: Minimality and equivalence
cites work: Linear Dynamical Systems and Instantons in Yang-Mills Theory
cites work: Q5638871
cites work: Descriptor representations without direct feedthrough term
cites work: Finite-dimensional time-invariant linear dynamical systems: Algebraic theory
cites work: Leverrier's algorithm for singular systems
cites work: Direct controllability and observability time domain conditions of singular systems
cites work: A general realization theory for higher-order linear differential equations
cites work: On behaviors and convolutional codes
cites work: Q3027143
cites work: Q4758117
cites work: Paradigms and puzzles in the theory of dynamical systems
full work available at URL: s0005-1098(96)00154-9
OpenAlex ID: W2117048623
description: scientific article; zbMATH DE number 1008758