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2003 | 13 | 1 | 15-27
Tytuł artykułu

Polynomial systems theory applied to the analysis and design of multidimensional systems

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
The use of a principal ideal domain structure for the analysis and design of multidimensional systems is discussed. As a first step it is shown that a lattice structure can be introduced for IO-relations generated by polynomial matrices in a signal space X (an Abelian group). It is assumed that the matrices take values in a polynomial ring F[p] where F is a field such that F[p] is a commutative subring of the ring of endomorphisms of X. After that it is analysed when a given F[p] acting on X can be extended to its field of fractions F(p). The conditions on the pair (F[p],X) are quite restrictive, i.e. each non-zero a(p)∊F[p] has to be an automorphism on X before the extension is possible. However, when this condition is met, say for operators {p1, p2, . . . , pn−1}, a polynomial ring F[p1, p2, . . . , pn] acting on X can be extended to F(p1, p2, . . . , pn−1)[pn], resulting in a principal ideal domain structure. Hence in this case all the rigorous principles of ‘ordinary’ polynomial systems theory for the analysis and design of systems is applicable. As an example, both an observer for estimating non-measurable outputs and a stabilizing controller for a distributed parameter system are designed.
Rocznik
Tom
13
Numer
1
Strony
15-27
Opis fizyczny
Daty
wydano
2003
otrzymano
2002-09-01
poprawiono
2003-01-01
Twórcy
autor
  • University of Oulu, Systems Engineering Laboratory, P.O. Box 4300, FIN90014, Finland
autor
  • University of Oulu, Systems Engineering Laboratory, P.O. Box 4300, FIN90014, Finland
Bibliografia
  • Blomberg H. and Ylinen R. (1983): Algebraic Theory for Multivariable Linear Systems. - London: Academic Press.
  • Hinrichsen D. and Pratzel-Wolters D. (1980): Solution modules and system equivalence. - Int. J. Contr., Vol. 32, No. 5, pp. 777-802.
  • Hatonen J. and Ylinen R. (2000): Synthesis of nD systems using polynomial approach. - Proc. 2nd Int. Workshop Multidimensional (nD) Systems, Czocha Castle, Poland, pp. 159-164.
  • Kučera V. (1979): Discrete Linear Control: The Polynomial Equation Approach. - New York: Wiley.
  • Morf M., Levy B., Kung S.Y. and Kailath T. (1977): New results in 2-D systems theory, Part I and II. - Proc. IEEE, Vol. 65, No. 6, pp. 861-872; 945-961.
  • Napoli M. and Zampieri S. (1999): Two-dimensional proper rational matrices and causal inputoutput representations of two-dimensional behavioral systems. - SIAM J. Contr. Opt., Vol. 37, No. 5, pp. 1538-1552.
  • Northcott D.G. (1968): Lessons on Rings, Modules and Multiplicities. - Cambridge: Cambridge University Press.
  • Oberst U. (1990): Multidimensional constant linear systems. - Acta Applicande Mathematicae, Vol. 20, pp. 1-175.
  • Rosenbrock H.H. (1970): State-Space and Multivariable Theory. -London: Nelson.
  • Valcher M.E. and Willems J.C. (1999): Observer synthesis in the behavioral approach. - IEEE Trans. Automat. Contr., Vol. AC-44, No. 12, pp. 2297-2307.
  • Willems J.C. (1991): Paradigms and puzzles in the theory of dynamic systems. - IEEE Trans. Automat. Contr., Vol. AC-36, No. 3, pp. 259-294.
  • Willems J.C. (1997): On interconnections, control and feedback. - IEEE Trans. Automat. Contr., Vol. AC-42, No. 3, pp. 326-339.
  • Wolovich W.A. (1974): Linear Multivariable Systems. - New York: Springer.
  • Wood J. (2000): Modules and behaviours in nD systems theory. - Multidimensional Syst. Signal Proc., Vol. 11, No. 1-2, pp. 11-48.
  • Ylinen R. (1975): On the algebraic theory of linear differential and difference systems with time-varying or operator coefficients. - Tech. Rep., Helsinki University of Technology, Systems Theory Laboratory, No. B23.
  • Ylinen R. (1980): An algebraic theory for analysis and synthesis of time-varying lineal differential systems. - Acta Polytechnica Scandinavica, No. Ma32.
  • Ylinen R. and Blomberg H. (1989): Order and equivalence relations on descriptions of finite dimensional linear system, In: Computer Aided Systems Theory-EUROCAST'89 (F. Pichler and R. Moreno Diaz, Eds.). - Berlin: Springer.
  • Zampieri S. (1998): Causal input/output representation of 2D systemsin the behavioral approach. - SIAM J. Contr. Opt., Vol. 36, No. 5, pp. 1133-1146.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-amcv13i1p15bwm
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