On Hyper–Regularity and Unimodularity of Ore Polynomial Matrices

Antritter, F., Cazaurang, F., Lévine, J. and Middeke, J. (2014). On the computation of π-flat outputs for linear time-varying differential-delay systems, Systems & Control Letters 71: 14-22.10.1016/j.sysconle.2014.07.002Search in Google Scholar

Antritter, F. and Middeke, J. (2011). A toolbox for the analysis of linear systems with delays, Proceedings of CDC-ECC, Orlando, FL, USA, pp. 1950-1955.10.1109/CDC.2011.6160636Search in Google Scholar

Beckermann, B., Cheng, H. and Labahn, G. (2006). Fraction-free row reduction of matrices of Ore polynomials, Journal of Symbolic Computation 41(5): 513-543.10.1016/j.jsc.2005.10.002Search in Google Scholar

Ben-Israel, A. and Greville, T.N. (2003). Generalized Inverses: Theory and Applications, Springer, New York, NY.Search in Google Scholar

Bose, N.K. and Mitra, S.K. (1978). Generalized inverse of polynomial matrices, IEEE Transactions on Automatic Control 23(3): 491-493.10.1109/TAC.1978.1101751Search in Google Scholar

Boullion, T.L. and Odell, P.L. (1971). Generalized Inverse Matrices, Wiley, New York, NY.Search in Google Scholar

Campbell, S.L. and Meyer, C.D. (2008). Generalized Inverses of Linear Transformations, SIAM, London.10.1137/1.9780898719048Search in Google Scholar

Cluzeau, T. and Quadrat, A. (2013). Isomorphisms and Serre’s reduction of linear systems, Proceedings of the 8th International Workshop on Multidimensional Systems, Erlangen, Germany, pp. 11-16.Search in Google Scholar

Cohn, P. (1985). Free Rings and Their Relations, Academic Press, London.Search in Google Scholar

Davies, P., Cheng, H. and Labahn, G. (2008). Computing Popov form of general Ore polynomial matrices, Proceedings of the Conference on Milestones in Computer Algebra (MICA), Stonehaven Bay, Trinidad and Tobago, pp. 149-156.Search in Google Scholar

Fabianska, A. and Quadrat, A. (2007). Applications of the Quillen-Suslin theorem to multidimensional systems theory, in H. Park and G. Regensburger (Eds.), Grӧbner Bases in Control Theory and Signal Processing, De Gruyter, Berlin/New York, NY, pp. 23-106.10.1515/9783110909746.23Search in Google Scholar

Franke, M. and Rӧbenack, K. (2013). On the computation of flat outputs for nonlinear control systems, Proceedings of the European Control Conference (ECC), Z¨urich, Switzerland, pp. 167-172.10.23919/ECC.2013.6669771Search in Google Scholar

Fritzsche, K. (2018). Toolbox for checking hyper regularity and unimodularity of polynomial matrices in the differential operator d/dt, https://github.com/klim-/hypore.10.2478/amcs-2018-0045Search in Google Scholar

Fritzsche, K., Knoll, C., Franke, M. and R¨obenack, K. (2016). Unimodular completion and direct flat representation in the context of differential flatness, Proceedings in Applied Mathematics and Mechanics 16(1): 807-808.10.1002/pamm.201610392Search in Google Scholar

Gupta, R.N., Khurana, A., Khurana, D. and Lam, T.Y. (2009). Rings over which the transpose of every invertible matrix is invertible, Journal of Algebra 322(5): 1627-1636.10.1016/j.jalgebra.2009.05.029Search in Google Scholar

Jacobson, N. (1953). Lectures in Abstract Algebra II: Linear Algebra, Springer, New York, NY.10.1007/978-1-4684-7053-6Search in Google Scholar

Knoll, C. (2016). Regelungstheoretische Analyse- und Entwurfsans ¨atze f¨ur unteraktuierte mechanische Systeme, PhD thesis, TU Dresden, Dresden.Search in Google Scholar

Knoll, C. and Fritzsche, K. (2017). Symbtools: A toolbox for symbolic calculations in nonlinear control theory, DOI: 10.5281/zenodo.275073.10.5281/zenodo.275073Open DOISearch in Google Scholar

Kondratieva, M.V., Mikhalev, A.V. and Pankratiev, E.V. (1982). On Jacobi’s bound for systems of differential polynomials, Algebra, Moscow University Press, Moscow, pp. 79-85.Search in Google Scholar

Lam, T. (1978). Serre’s Conjecture, Springer, Berlin/Heidelberg.Search in Google Scholar

Lévine, J. (2011). On necessary and sufficient conditions for differential flatness, Applicable Algebra in Engineering, Communication and Computing 22(1): 47-90.10.1007/s00200-010-0137-xSearch in Google Scholar

Logar, A. and Sturmfels, B. (1992). Algorithms for the Quillen-Suslin theorem, Journal of Algebra 145(1): 231-239.10.1016/0021-8693(92)90189-SSearch in Google Scholar

Meurer, A., Smith, C., Paprocki, M., ˇ Cert´ık, O., Kirpichev, S., Rocklin, M., Kumar, A., Ivanov, S., Moore, J., Singh, S., Rathnayake, T., Vig, S., Granger, B., Muller, R., Bonazzi, F., Gupta, H., Vats, S., Johansson, F., Pedregosa, F., Curry, M., Terrel, A., Rouˇcka, v., Saboo, A., Fernando, I., Kulal, S., Cimrman, R. and Scopatz, A. (2017). SymPY: Symbolic computing in Python, PeerJ Computer Science 3: e103, DOI: 10.7717/peerj-cs.103.10.7717/peerj-cs.103Open DOISearch in Google Scholar

Middeke, J. (2011). A Computational View on Normal Forms of Matrices of Ore Polynomials, PhD thesis, Johannes Kepler Universit¨at Linz, Linz.Search in Google Scholar

Newman, M. (1972). Integral Matrices, Academic Press, New York, NY/London.Search in Google Scholar

Ollivier, F. (1990). Standard bases of differential ideals, Proceedings of the 8th International Conference on Applied Algebra, Algebraic Algorithms and Error-Correcting10.1007/3-540-54195-0_60Search in Google Scholar

Codes, Tokyo, Japan, pp. 304-321. Ollivier, F. and Brahim, S. (2007). La borne de Jacobi pour une diffi´et´e d´efinie par un syst`eme quasi r´egulier (Jacobi’s bound for a diffiety defined by a quasi-regular system), Comptes rendus Math´ematiques 345(3): 139-144.10.1016/j.crma.2007.06.010Search in Google Scholar

Ritt, J.F. (1935). Jacobi’s problem on the order of a system of differential equations, Annals of Mathematics 36(2): 303-312.10.2307/1968572Search in Google Scholar

Rӧbenack, K. and Reinschke, K. (2011). On generalized inverses of singular matrix pencils, International Journal of Applied Mathematics and Computer Science 21(1): 161-172, DOI: 10.2478/v10006-011-0012-3.10.2478/v10006-011-0012-3Open DOISearch in Google Scholar

Verhoeven, G.G. (2016). Symbolic Software Tools for Flatness of Linear Systems with Delays and Nonlinear Systems, PhD thesis, Universit¨at der Bundeswehr M¨unchen, Munich.Search in Google Scholar

Youla, D. and Pickel, P. (1984). The Quillen-Suslin theorem and the structure of n-dimensional elementary polynomial matrices, IEEE Transactions on Circuits and Systems 31(6): 513-518.10.1109/TCS.1984.1085545Search in Google Scholar

Zhou, W. and Labahn, G. (2014). Unimodular completion of polynomial matrices, Proceedings of the 41st International Symposium on Symbolic and Algebraic Computation (ISSAC), Kobe, Japan, pp. 414-420.10.1145/2608628.2608640Search in Google Scholar