Article
Full entry |
PDF
(1.3 MB)
Feedback
PDF
(1.3 MB)
Feedback
Keywords:
coprime polynomial fraction; transfer function matrix; polynomial matrix; Markov matrices; state-space model
coprime polynomial fraction; transfer function matrix; polynomial matrix; Markov matrices; state-space model
Summary:
A new form of the coprime polynomial fraction $C(s)\,F(s)^{-1}$ of a transfer function matrix $G(s)$ is presented where the polynomial matrices $C(s)$ and $F(s)$ have the form of a matrix (or generalized matrix) polynomials with the structure defined directly by the controllability characteristics of a state- space model and Markov matrices $HB$, $HAB$, ...
References:
[1] Asseo S. J.: Phase-variable canonical transformation of multicontroller system. IEEE Trans. Automat. Control AC–13 (1968), 129–131 DOI 10.1109/TAC.1968.1098823
[2] Gohberg I., Lancaster, P., Rodman L.: Matrix Polynomial. Academic Press, New York 1982 MR 0662418
[3] Davison E. J., Wang S. H.: Property and calculation of transmission zeros of linear multivariable systems. Automatica 10 (1974), 643–658 DOI 10.1016/0005-1098(74)90085-5
[4] Desoer C. A., Vidyasagar M.: Feedback Systems: Input-Output Properties. Academic Press, New York 1975 MR 0490289 | Zbl 1153.93015
[5] Isidori A.: Nonlinear Control Systems. Springer, New York 1995 MR 1410988 | Zbl 0931.93005
[6] Kailath T.: Linear Systems. Prentice–Hall, Englewood Cliffs, N.J. 1980 MR 0569473 | Zbl 0870.93013
[7] Kwakernaak H.: Progress in the polynomial solution in the standart $H^{\infty }$ problem. In: Proc. 11 IFAC Congress, Tallinn 1990, 5, pp. 122–129
[8] Kučera V.: Discrete Linear Control – The Polynomial Equation Approach. Academia, Prague 1979 MR 0573447 | Zbl 0432.93001
[9] Resende P., Silva V. V. R.: On the modal order reduction of linear multivariable systems using a block-Schwartz realization. In: Proc. 11 IFAC Congress, Tallinn 1990, 2, pp. 266–270
[10] Rosenbrock H. H.: State Space and Multivariable Theory. Thomas Nelson, London 1970 MR 0325201 | Zbl 0246.93010
[11] Smagina, Ye. M.: Problems of Linear Multivariable System Analysis Using the Concept of System Zeros. Tomsk University, Tomsk 1990
[12] Smagina, Ye. M.: Definition, Determination and Application of System Zeros. Doct. Sci. Thesis, Tomsk 1994
[13] Smagina, Ye. M.: New approach to transfer function matrix factorization. In: Proc. 1997 IFAC Conference on Control of Industrial Systems, Pergamon France 1997, 1, pp. 307–312
[14] Stefanidis P., Paplinski A. P., Gibbard M. J.: Numerical operations with polynomial matrices (Lecture Notes in Control and Inform. Sciences 171). Springer, Berlin 1992 MR 1151835
[15] Tokarzewski J.: System zeros analysis via the Moore-Penrose pseudoinverse and SVD of the first nonzero Markov parameters. IEEE Trans. Automat. Control AC–43 (1998), 1285–1288 DOI 10.1109/9.718619 | MR 1640160
[16] Wolovich W. A.: On the numerators and zeros of rational transfer matrices. IEEE Trans. Automat. Control AC–18 (1973), 544–546 DOI 10.1109/TAC.1973.1100393 | MR 0441440 | Zbl 0266.93017
[17] Wolovich W. A.: Linear Multivariable Systems. Springer, New York 1974 MR 0359881 | Zbl 0534.93026
[18] Youla D. C., Jarb H. A., Bongiorno J. J.: Modern Wiener-Hopf design of optimal controller. Part 2: The multivariable case. IEEE Trans. Automat. Control AC–21 (1976), 319–338 DOI 10.1109/TAC.1976.1101223 | MR 0446637
[19] Yokoyama R., Kinnen E.: Phase-variable canonical forms for the multi-input, multi-output systems. Internat. J. Control 17 (1976), 1297–1312 DOI 10.1080/00207177308932475 | MR 0335019
Search
Partner of
