PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
2001 | 11 | 5 | 1055-1068
Tytuł artykułu

Computing generalized inverse systems using matrix pencil methods

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We address the numerically reliable computation of generalized inverses of rational matrices in descriptor state-space representation. We put particular emphasis on two classes of inverses: the weak generalized inverse and the Moore-Penrose pseudoinverse. By combining the underlying computational techniques, other types of inverses of rational matrices can be computed as well. The main computational ingredient to determine generalized inverses is the orthogonal reduction of the system matrix pencil to appropriate Kronecker-like forms.
Rocznik
Tom
11
Numer
5
Strony
1055-1068
Opis fizyczny
Daty
wydano
2001
Twórcy
autor
  • German Aerospace Center, DLR - Oberpfaffenhofen, Institute of Robotics and Mechatronics, D-82234 Wessling, Germany
Bibliografia
  • Antsaklis P. (1978): Stable proper nth-order inverses. — IEEE Trans. Automat. Contr., Vol.23, No.6, pp.1104–1106.
  • Ben Israel A. and Greville T.N.E. (1976): Some topics in generalized inverses of matrices, In: Generalized Inverses and Applications (M.Z. Nashed, Ed.). — New York: Academic Press, pp.125–147.
  • Benner P., Mehrmann V., Sima V., Van Huffel S. and Varga A. (1999): SLICOT—A subroutine library in systems and control theory, In: Applied and Computational Control, Signals and Circuits (B.N. Datta, Ed.). — Boston: Birkhäuser, Vol.1, pp.499–539.
  • Campbell S.L. and Meyer C.D. (1991): Generalized Inverses of Linear Transformations. — New York: Dover Publications, Inc.
  • Campbell S.L. and Rakowski M. (1994): Explicit formulae for completions of linear time varying DAEs. — Circ. Syst. Signal Process., Vol.13, No.2–3, pp.185–199.
  • Misra P., Van Dooren P. and Varga A. (1994): Computation of structural invariants of generalized state-space systems. — Automatica, Vol.30, No.12, pp.1921–1936.
  • Morse A.S. (1976): Minimal solutions to transfer matrix equations. — IEEE Trans. Automat. Contr., Vol.21, No.1, pp.131–133.
  • Oară C. and Varga A. (1999): The general inner-outer factorization problem for discrete-time systems. — Proc. ECC’99, Karlsruhe, Germany, (published on CD-ROM).
  • Oară C. and Varga A. (2000): Computation of general inner-outer and spectral factorizations. — IEEE Trans. Automat. Contr., Vol.45, No.12, pp.2307–2325.
  • Oară C. (2000): A QR factorization of a rational matrix: The class of solutions and applications in systems theory. — Proc. MTNS 2000, Perpignan, France (published on CD-ROM).
  • Rakowski M. (1991): Generalized pseudoinverses of matrix valued functions. — Int. Eqns. Oper. Theory, Vol.14, No.4, pp.564–585.
  • Sontag E. (1980): On generalized inverses of polynomial and other matrices. — IEEE Trans. Automat. Contr., Vol.25, No.3, pp.514–517.
  • Varga A. (1995): On stabilization of descriptor systems. — Syst. Contr. Lett., Vol.24, No.2, pp.133–138.
  • Varga A. (1996): Computation of Kronecker-like forms of a system pencil: Applications, algorithms and software. — Proc. CACSD’96 Symposium, Dearborn, MI, pp.77–82.
  • Varga A. (1998): Computation of inner-outer factorizations of rational matrices. — IEEE Trans. Automat. Contr., Vol.43, No.5, pp.684–688.
  • Varga A. (2000): A descriptor systems toolbox for Matlab. — Proc. CACSD 2000 Symposium, Anchorage, Alaska.
  • Varga A. and Katayama T. (1998): Computation of J-inner-outer factorizations of rational matrices. — Int. J. Robust Nonlin. Contr., Vol.8, No.3, pp.245–263.
  • Wang S.-H. and Davison E.J. (1973): A minimization algorithm for the design of linear multivariable systems. — IEEE Trans. Automat. Contr., Vol.18, No.3, pp.220–225.
  • Wolovich W.A., Antsaklis P. and Elliott H. (1977): On the stability of solutions to minimal and nonminimal design problems. — IEEE Trans. Automat. Contr., Vol.22, No.1, pp.88– 94.
  • Wonham W.M. (1979): Linear Multivariable Control: a Geometric Approach. — New York: Springer Verlag.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-amcv11i5p1055bwm
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.