An efficient computation of the solution of the block decoupling problem with coefficient assignment over a ring. (English) Zbl 1274.93087

Summary: The paper presents procedures to check solvability and to compute solutions to the block decoupling problem over a Noetherian ring and procedures to compute a feedback law that assigns the coefficients of the compensated system while maintaining the decoupled structure over a principal ideal domain. The algorithms have been implemented using Maple V and CoCoA [A. Capani, G. Niesi and L. Robbiano, “CoCoA, a system for doing computations in commutative algebra”, available via anonymous ftp from: CoCoA.dima.unige.it].


93B40 Computational methods in systems theory (MSC2010)
93B25 Algebraic methods


Maple; CoCoA
Full Text: Link


[1] Adams W. W., Loustaunau P.: An introduction to Gröbner bases. (Graduate Studies in Mathematics 3.) Amer. Math. Soc. 1996 · Zbl 0803.13015
[2] Assan J., Lafay J. F., Perdon A. M.: An algorithm to compute maximal pre-controllability submodules over a Principal Ideal Domain. Proc. IFAC Workshop on Linear Time Delay Systems, Grenoble 1998, pp. 123-128
[3] Assan J., Lafay J. F., Perdon A. M.: Computation of maximal pre-controllability submodules over a Noetherian ring (to appear. · Zbl 0917.93024 · doi:10.1016/S0167-6911(99)00015-8
[4] Basile G., Marro G.: Controlled and Conditioned Invariants in Linear System Theory. Prentice Hall, Englewood Cliffs, N. J. 1992 · Zbl 0758.93002
[5] Brewer J. W., Klinger L. C., Schmale W.: The dynamic feedback cyclization problem for Principal Ideal Domains. J. Pure Appl. Algebra (1994), 31-42 · Zbl 0838.93030
[6] Buchberger B.: Ein Algorithmus zum Auffinden der Basiselemente des Restklassenringes nach einem nulldimensionalen Polynomideal. Ph.D. Thesis, University of Innsbruck, Innsbruck 1965 · Zbl 1245.13020
[7] Conte G., Perdon A. M.: The disturbance decoupling problem for systems over a ring. SIAM J. Control Optim. 33 (1995), 3, 750-764 · Zbl 0831.93011 · doi:10.1137/S0363012992235638
[8] Conte G., Perdon A. M.: The block decoupling problem for systems over a ring. IEEE Trans. Automat. Control 43 (1998), 11, 1600-1604 · Zbl 0964.93025 · doi:10.1109/9.728878
[9] Conte G., Perdon A. M., Lombardo A.: Block decoupling problem with coefficient assignment and stability for linear systems over Noetherian rings. Proc. IFAC Conference on System Structure and Control, Nantes 1998 · Zbl 1017.93505
[10] Emre E., Khargonekar P.: 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
[11] Dübbelde J., Schmale W.: Normalformproblem und Koefficientenzuweisung bei Systemen über euklidischen Ringen. University of Oldenburg, 1994
[12] Hautus M. L. J.: Disturbance rejection for systems over rings. (Lecture Notes in Control and Infomation Sciences 58.) Springer-Verlag, Berlin 1984 · Zbl 0532.93044 · doi:10.1007/BFb0031071
[13] Inaba H., Ito N., Munaka T.: Decoupling and pole assignment for linear systems defined over a Principal Ideal Domain. Linear Circuits, Systems and Signal Processing: Theory and Applications (C. I. Byrnes, C. F. Martin, R. E. Saeks, North Holland, Amsterdam 1988 · Zbl 0675.93017
[14] Lang S.: Algebra. Second edition. Addison Wesley, Reading 1984 · Zbl 1063.00002
[15] Sename O., Lafay J. F.: Decoupling of square linear systems with delays. IEEE Trans. Automat. Control 42 (1997), 5, 736-742 · Zbl 0910.93039 · doi:10.1109/9.580895
[16] Wonham M.: Linear Multivariable Control: A Geometric Approach. Third edition. Springer-Verlag, New York 1985 · Zbl 0609.93001
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