Sebek, Michael 2-D polynomial equations. (English) Zbl 0515.93036 Kybernetika 19, 212-224 (1983). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 1 ReviewCited in 4 Documents MSC: 93C35 Multivariable systems, multidimensional control systems 12E12 Equations in general fields 93B40 Computational methods in systems theory (MSC2010) 26C99 Polynomials, rational functions in real analysis Keywords:two-dimensional polynomial equations; minimum degree solution; computational algorithm × Cite Format Result Cite Review PDF Full Text: EuDML References: [1] E. Bertini: Zum Fundamentalsatz aus der Theorie der algebraischen Funktionen. Math. Ann. 34 (1889), 447-449. · JFM 21.0426.02 [2] N. K. Bose: Multidimensional Systems: Theory and Applications. IEEE Press, New York 1979. · Zbl 0399.90001 [3] R. Eising: 2-D Systems - An Algebraic Approach. Ph. D. Dissertation, Eindhoven University of Technology, Eindhoven 1979. · Zbl 0426.93028 [4] E. Emre: The polynomial equation \(QQ_c + RP_c = \emptyset\) with application to dynamic feedback. SIAM J. Control Optim. 18 (1980), 6, 611-620. · Zbl 0505.93016 · doi:10.1137/0318045 [5] E. Emre, P. P. Khargonekar: Regulation of split linear systems over rings: coefficient-assignment and observers. IEEE Trans. Automat. Control AC-27 (1982), 1, 104-113. · Zbl 0502.93019 · doi:10.1109/TAC.1982.1102815 [6] T. Kailath: Linear Systems. Prentice-Hall, Englewood Cliffs 1980. · Zbl 0454.93001 [7] E. W. Kamen: A note on the representation of lumped-distributed networks, delay-differential systems and 2-D systems. IEEE Trans. Circuits and Systems CAS-27 (1980), 5, 430-432. [8] E. W. Kamen: Linear systems with comensurate time delays: stability and stabilization independent of delay. IEEE Trans. Automat. Control AC-27 (1982), 2, 367-375. · Zbl 0517.93047 · doi:10.1109/TAC.1982.1102916 [9] V. Kučera: Discrete Linear Control: The Polynomial Equation Approach. Wiley, Chichester 1979. [10] A. S. Morse: Ring models for delay-differential systems. Automatica 12 (1976), 5, 529-531. · Zbl 0345.93023 · doi:10.1016/0005-1098(76)90013-3 [11] M. Noether: Über einen Satz aus der Theorie der algebraischen Funktionen. Math. Ann. 6 (1873), 351-359. [12] A. W. Olbrot, S. H. Żak: Controllability and observability problems for linear functional-differential systems. Foundations of Control Engineering 5 (1980), 2, 79 - 89. · Zbl 0432.93006 [13] P. N. Paraskevopoulos: Feedback design techniques for linear multivariable 2-D systems. Analysis and Optimization of Systems (A. Bensoussan and J. L. Lions, Springer-Verlag, Berlin-Heidelberg-New York 1980. [14] Special issue on multidimensional systems. Proc. IEEE 65 (1977), 6. · Zbl 1170.01341 [15] M. Šebek: 2-D Exact model matching. IEEE Trans. Automat. Control AC-28 (1983), 2, 215-217. [16] L. N. Volgin: The Fundamentals of the Theory of Controlling Machines. (in Russian). Soviet Radio, Moscow 1962. [17] B. L. van der Waerden: Modern Algebra. 4th (2 volumes). Frederic Ungar Publishing Co., New York 1964. [18] W. A. Wolovich: Linear Multivariable Systems. Springer-Verlag, New York-Heidelberg-Berlin 1974. · Zbl 0291.93002 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.