PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
2001 | 11 | 6 | 1249-1260
Tytuł artykułu

Factorization of the Popov function of a multivariable linear distributed parameter system in the non-coercive case: a penalization approach

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We study the construction of an outer factor to a positive definite Popov function of a distributed parameter system. We assume that is a non-negative definite matrix with non-zero determinant. Coercivity is not assumed. We present a penalization approach which gives an outer factor just in the case when there exists any outer factor.
Rocznik
Tom
11
Numer
6
Strony
1249-1260
Opis fizyczny
Daty
wydano
2001
Twórcy
  • Politecnico di Torino, Dipartimento di Matematica, Corso Duca degli Abruzzi, 24, 10129 Torino, Italy
Bibliografia
  • Anderson B.D.O. (1967): A system theory criterion for positive real matrices. — SIAM J. Contr., Vol.5, pp.171–182.
  • Anderson B.D.O. and Vongpanitlered S. (1973): Network Analysis and Synthesis: A Modern Systems Theory Approach. — Englewood Cliffs, N.J: Prentice–Hall.
  • Balakrishnan A.V. (1995): On a generalization of the Kalman–Yakubovich Lemma. — Appl. Math. Optim., Vol.31, No.2, pp.177–187.
  • Callier F.M. and Winkin J. (1990): On spectral factorization and LQ-optimal regulation for multivariable distributed systems. — Int. J. Contr., Vol.52, No.1, pp.55–75.
  • Callier F.M. and Winkin J. (1992): LQ-optimal control of infinite-dimensional systems by spectral factorization. — Automatica, Vol.28, No.4, pp.757–770.
  • Callier F.M. and Winkin J. (1999): The spectral factorization problem for multivariable distributed parameter systems. — Int. Eqns. Oper. Theory, Vol.34, No.3, pp.270–292.
  • Fattorini O. (1968): Boundary control systems. — SIAM J. Contr. Optim., Vol.6, pp.349–385.
  • Francis B.A., (1987): A Course in H∞ Control Theory. — Berlin: Springer-Verlag.
  • Garnett J.B., (1981): Bounded Analytic Functions. — New York: Academic Press.
  • Kalman R.E. (1963): Lyapunov functions for the problem of Lur’e in automatic control. — Proc. Nat. Acad. Sci., USA, Vol.49, pp.201–205.
  • Lasiecka I. and Triggiani R. (2000): Control theory for partial differential equations. — Encyclopaedia of Mathematics and its Applications, Vols. 74 and 75, Cambridge: Cambridge University Press.
  • Louis J-Cl. and Wexler D. (1991): The Hilbert space regulator problem and operator Riccati equation under stabilizability. — Annales de la Soc. Scient. de Bruxelles, Vol.105, No.4, pp.137–165.
  • Nikolski N. (1982): Lectures on the Shift Operator. — Berlin: Springer-Verlag.
  • Pandolfi L. (1994): From singular to regular control systems. — Proc. Conf. Control of Partial Differential Equations, New York: M. Dekker, pp.153–165.
  • Pandolfi L. (1995): The standard regulator problem for systems with input delays: an approach through singular control theory. — Appl. Math. Optim., Vol.31, No.2, pp.119–136. Pandolfi L. (1997): The Kalman–Yakubovich–Popov Theorem: an overview and new results for hyperbolic control systems. — Nonlin. Anal., Vol.30, No.2, pp.735–745.
  • Pandolfi L. (1998): Dissipativity and Lur’e problem for parabolic boundary control systems. — SIAM J. Contr. Optim., Vol.36, No.6, pp.2061–2081.
  • Pandolfi, L. (1999a): The Kalman-Yakubovich-Popov theorem for stabilizable hyperbolic boundary control systems. — Int. Eqns. Oper. Theory, Vol.34, pp.478–493.
  • Pandolfi L. (1999b): Recent results on the Kalman-Popov-Yakubovich problem. — Proc. Int. Conf. Mathematics and its Applications, Yogyakarta, Indonesia, pp.47–60.
  • Rosenblum M. and Rovnyak J. (1985): Hardy Classes and Operator Theory. — New York: Oxford U.P.
  • Riesz F. and Sz-Nagy B. (1955): Functional Analysis. — New York: F. Ungar.
  • Yakubovich V.A. (1973): The frequency theorem in control theory. — Siberian Math. J., Vol.14, pp.384-419.
  • Youla D.C. (1961): On the factorization of rational matrices. — IRE Trans. Inf. Theory, Vol.IT–7, pp.172–189.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-amcv11i6p1249bwm
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.