34
Views
6
CrossRef citations to date
0
Altmetric
Original Articles

Equivalence transformations of rational matrices and applications

, &
Pages 1001-1020 | Received 07 Jul 1992, Published online: 15 Mar 2007

REFERENCES

  • ANDERSON , B. D. O. , COPPEL , W. A. , and CULLEN , D. J. , 1985 , Strong system equivalence (I) . Journal of the Australian Mathematical Societies, Series B , 27 , 194 – 222 .
  • CULLEN , J. , 1987 , Underlying algebraic framework of equivalence relations on linear systems . International Journal of Control , 45 , 1415 – 1425 .
  • HAYTON , G. E. , PUGH , A. C. and FRETWELL , P. , 1988 , Infinite elementary divisors of a matrix polynomial and implications . International Journal of Control , 47 , 53 – 64 .
  • KAILATH , T. , 1980 , Linear Systems ( Englewood Cliffs , NJ : Prentice Hall ).
  • PERNEBO , L. , 1981 , An algebraic theory for the design of controllers for linear multivariable systems-Part I . IEEE Transactions on Automatic Control , 26 , 171 – 182 .
  • PUGH , A. C. , JOHNSON , D. S. , and HAYTON , G. E. , 1992 , On conditions guaranteeing two polynomial matrices possess identical zero structures . IEEE Transactions on Automatic Control , 37 , 1383 – 1386 .
  • PUGH , A.C. , JONES , E. R. L. , DEMIANCZUK , O. and HAYTON , G. E. , 1989 , Infinite frequency structure and a certain matrix laurent expansion . International Journal of Control , 50 , 1793 – 1805 .
  • PUGH , A. C. , and RATCLIFFE , P. A. , 1980 , Infinite frequency interpretations of minimal bases . International Journal of Control , 32 , 581 – 588 .
  • PUGH , A. C. , and SHELTON , A. K. , 1978 , On a new definition of strict system equivalence . International Journal of Control , 27 , 657 – 672 .
  • ROSENBROCK , H. H. , 1970 , State Space and Multivariable Theory ( London , U.K. : Nelson ).
  • VARDULAKIS , A. I. , 1991 , Linear Multivariable Control, Algebraic Analysis and Synthesis Methods ( London , U.K. : Nelson-Wiley ).
  • VARDULAKIS , A. I. , and KARCANIAS , N. , 1983 , Structure and Smith-McMillan form and coprime MFDs of a rational matrix inside a region P = Ω ∪ {∞} . International Journal of Control , 38 , 927 – 957 .
  • VARDULAKIS , A. I. G. , LIMEBEER , D. J. N. and KARCANIAS , N. , 1982 , Structure and Smith-McMillan form of a rational matrix at infinity , International Journal of Control , 35 , 701 – 725 .
  • VERGHESE , G. C. , 1979 , Infinite frequency behaviour in generalized dynamical systems . Ph.D. dissertation , Stanford University , Stanford , California , U.S.A .
  • VERGHESE , G. C. , and KAILATH , T. , 1981 , Rational matrix structure . IEEE Transactions on Automatic Control , 26 , 434 – 439 .
  • WALKER , A. B. , 1988 , Equivalence transformations for linear systems . Ph.D. dissertation , The University of Hull , U.K.
  • ZHANG , S.-Y. , 1989 a , Generalised proper inverse of polynomial matrices and the existence of infinite decoupling zeros . IEEE Transactions on Automatic Control , 34 , 743 – 745 . 1989 b, Polynomial matrix linearization and strongly irreducible realization for singular systems. International Journal of Control, 49, 471–479 .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.