Summary
The purpose of this paper is to demonstrate the symbolic package OREMORPHISMS which is dedicated to the implementation of different algorithms and heuristic methods for the study of the factorization, reduction and decomposition problems of general linear functional systems (e.g., systems of partial differential or difference equations, differential time-delay systems). In particular, we explicitly show how to decompose a differential timedelay system (a string with an interior mass [15]) formed by 4 equations in 6 unknowns and prove that it is equivalent to a simple equation in 3 unknowns. We finally give a list of reductions of classical systems of differential time-delay equations and partial differential equations coming from control theory and mathematical physics.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Barakat, M., Robertz, D.: An abstract package for homological algebra. J. Algebra Appl. 7, 299–317 (2008), http://wwwb.math.rwth-aachen.de/homalg/
OreModules project, http://wwwb.math.rwth-aachen.de/OreModules
Chyzak, F., Quadrat, A., Robertz, D.: Effective algorithms for parametrizing linear control systems over Ore algebras. Appl. Algebra Engrg. Comm. Comput. 16, 319–376 (2005)
Chyzak, F., Quadrat, A., Robertz, D.: OreModules: A symbolic package for the study of multidimensional linear systems. In: Chiasson, J., Loiseau, J.J. (eds.) Applications of Time-Delay Systems. LNCIS, vol. 352, pp. 233–264. Springer, Heidelberg (2007)
Cluzeau, T., Quadrat, A.: Factoring and decomposing a class of linear functional systems. Linear Algebra Appl. 428, 324–381 (2008)
Cluzeau, T., Quadrat, A.: On algebraic simplifications of linear functional systems. In: Loiseau, J.J., Michiels, W., Niculescu, S.I., Sipahi, R. (eds.) Topics in Time-Delay Systems: Analysis, Algorithms and Control. LNCIS, pp. 167–178. Springer, Heidelberg (2009)
Cluzeau, T., Quadrat, A.: OreMorphisms project, http://www.ensil.unilim.fr/~cluzeau/ , http://www-sop.inria.fr/personnel/Alban.Quadrat/index.html
Courant, R., Hilbert, D.: Methods of Mathematical Physics. Wiley Classics Library, Wiley (1989)
Culianez, G.: Formes de Hermite et de Jacobson: Implémentations et applications. Internship with Quadrat A, INRIA Sophia Antipolis (2005)
Fabiańska, A.: QuillenSuslin project, http://wwwb.math.rwth-aachen.de/QuillenSuslin
Fabiańska, A., Quadrat, A.: Applications of the Quillen-Suslin theorem in multidimensional systems theory. In: Park, H., Regensburger, G. (eds.) Gröbner Bases in Control Theory and Signal Processing. Radon Series on Computation and Applied Mathematics, vol. 3, pp. 23–106. de Gruyter publisher (2007)
Kwakernaak, H., Sivan, R.: Linear Optimal Control Systems. Wiley, Chichester (1972)
Manitius, A.: Feedback controllers for a wind tunnel model involving a delay: analytical design and numerical simulations. IEEE Trans. Autom. Contr. 29, 1058–1068 (1984)
Mounier, H., Rudolph, J., Petitot, M., Fliess, M.: A flexible rod as a linear delay system. In: Proc. European Control Conference (ECC), Rome (1995)
Mounier, H., Rudolph, J., Fliess, M., Rouchon, P.: Tracking control of a vibrating string with an interior mass viewed as delay system. ESAIM Control Optim. Calc. Var. 3, 315–321 (1998)
Petit, N., Rouchon, P.: Dynamics and solutions to some control problems for water-tank systems. IEEE Trans. Automatic Control 47, 595–609 (2002)
Quadrat, A.: The fractional representation approach to synthesis problems: an algebraic analysis viewpoint. Part II: Internal stabilization, SIAM J. Control & Optimization 42, 300–320 (2003)
Quadrat, A., Robertz, D.: Computation of bases of free modules over the Weyl algebras. Journal Symbolic Comput. 42, 1113–1141 (2007)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Cluzeau, T., Quadrat, A. (2009). OreMorphisms: A Homological Algebraic Package for Factoring, Reducing and Decomposing Linear Functional Systems. In: Loiseau, J.J., Michiels, W., Niculescu, SI., Sipahi, R. (eds) Topics in Time Delay Systems. Lecture Notes in Control and Information Sciences, vol 388. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02897-7_16
Download citation
DOI: https://doi.org/10.1007/978-3-642-02897-7_16
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-02896-0
Online ISBN: 978-3-642-02897-7
eBook Packages: EngineeringEngineering (R0)