Construction of Algebraic and Difference Equations with a Prescribed Solution Space

Antoniou, E., Vardulakis, A. and Karampetakis, N. (1998). A spectral characterization of the behavior of discrete time AR-representations over a finite time interval, Kybernetika34(5): 555–564.10.23919/ECC.1997.7082163Search in Google Scholar

Antoulas, A. and Willems, J. (1993). A behavioral approach to linear exact modeling., IEEE Transactions on Automatic Control38(12): 1776–1802.Search in Google Scholar

Antsaklis, P.J. and Michel, A.N. (2006). Linear Systems, 2nd Edn., Birkhäuser, Boston, MA.Search in Google Scholar

Bernstein, D.S. (2009). Matrix Mathematics. Theory, Facts, and Formulas, 2nd Edn., Princeton University Press, Princeton, NJ.10.1515/9781400833344Search in Google Scholar

Campbell, S. (1980). Singular Systems of Differential Equations, Vol. 1, Research Notes in Mathematics, Pitman, London.Search in Google Scholar

Gantmacher, F.R. (1959). The Theory of Matrices, Vols. 1, 2, Chelsea Publishing Co., New York, NY.Search in Google Scholar

Gohberg, I., Lancaster, P. and Rodman, L. (2009). Matrix Polynomials, Reprint, SIAM, Philadelphia, PA.10.1137/1.9780898719024Search in Google Scholar

Hayton, G., Pugh, A. and Fretwell, P. (1988). Infinite elementary divisors of a matrix polynomial and implications, International Journal of Control47(1): 53–64.10.1080/00207178808905995Search in Google Scholar

Kaczorek, T. (2007). Polynomial and Rational Matrices. Applications in Dynamical Systems Theory, Springer, Dordrecht.10.1007/978-1-84628-605-6Search in Google Scholar

Kaczorek, T. (2014). Minimum energy control of fractional descriptor positive discrete-time linear systems, International Journal of Applied Mathematics and Computer Science24(4): 735–743, DOI: 10.2478/amcs-2014-0054.10.2478/amcs-2014-0054Search in Google Scholar

Kaczorek, T. (2015). Analysis of the descriptor Roesser model with the use of the Drazin inverse, International Journal of Applied Mathematics and Computer Science25(3): 539–546, DOI: 10.1515/amcs-2015-0040.10.1515/amcs-2015-0040Search in Google Scholar

Karampetakis, N.P. (2004). On the solution space of discrete time AR-representations over a finite time horizon, Linear Algebra and Its Applications382: 83–116.10.1016/j.laa.2003.11.026Search in Google Scholar

Karampetakis, N.P. (2015). Construction of algebraic-differential equations with given smooth and impulsive behaviour, IMA Journal of Mathematical Control and Information32(1): 195–224.10.1093/imamci/dnt041Search in Google Scholar

Karampetakis, N.P. and Vologiannidis, S. (2003). Infinite elementary divisor structure-preserving transformations for polynomial matrices, International Journal of Applied Mathematics and Computer Science13(4): 493–503.Search in Google Scholar

Karampetakis, N., Vologiannidis, S. and Vardulakis, A. (2004). A new notion of equivalence for discrete time AR representations, International Journal of Control77(6): 584–597.10.1080/002071709410001703223Search in Google Scholar

Markovsky, I., Willems, J.C., Van Huffel, S. and De Moor, B. (2006). Exact and Approximate Modeling of Linear Systems. A Behavioral Approach, SIAM, Philadelphia, PA.10.1137/1.9780898718263Search in Google Scholar

Praagman, C. (1991). Invariants of polynomial matrices, Proceedings of the 1st European Control Conference, Grenoble, France, pp. 1274–1277.Search in Google Scholar

Vardulakis, A. (1991). Linear Multivariable Control. Algebraic Analysis and Synthesis Methods, John Wiley & Sons, Chichester.Search in Google Scholar

Vardulakis, A., Limebeer, D. and Karcanias, N. (1982). Structure and Smith–MacMillan form of a rational matrix at infinity, International Journal of Control35(4): 701–725.10.1080/00207178208922649Search in Google Scholar

Willems, J.C. (1986). From time series to linear system, II: Exact modelling, Automatica22(6): 675–694.10.1016/0005-1098(86)90005-1Search in Google Scholar

Willems, J.C. (1991). Paradigms and puzzles in the theory of dynamical systems, IEEE Transansactions on Automatic Control36(3): 259–294.10.1109/9.73561Search in Google Scholar

Willems, J.C. (2007). Recursive computation of the MPUM, in A. Chiuso et al. (Eds.), Modeling, Estimation and Control, Springer, Berlin, pp. 329–344.10.1007/978-3-540-73570-0_25Search in Google Scholar

Zaballa, I. and Tisseur, F. (2012). Finite and infinite elementary divisors of matrix polynomials: A global approach, MIMS EPrint 2012.78, Manchester Institute for Mathematical Sciences, University of Manchester, Manchester.Search in Google Scholar

Zerz, E. (2008a). Behavioral systems theory: A survey, International Journal of Applied Mathematics and Computer Science18(3): 265–270, DOI: 10.2478/v10006-008-0024-9.10.2478/v10006-008-0024-9Search in Google Scholar

Zerz, E. (2008b). The discrete multidimensional MPUM, Multidimensional System Signal Processing19(3–4): 307–321.10.1007/s11045-007-0043-ySearch in Google Scholar

Zerz, E., Levandovskyy, V. and Schindelar, K. (2011). Exact linear modeling with polynomial coefficients, Multidimensional System Signal Processing22(1–3): 55–65.10.1007/s11045-010-0125-0Search in Google Scholar