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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

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  • 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.
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  • 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.
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Bibliografia

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