PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
2001 | 11 | 6 | 1387-1403
Tytuł artykułu

Circle criterion and boundary control systems in factor form: input-output approach

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
A circle criterion is obtained for a SISO Lur’e feedback control system consist- ing of a nonlinear static sector-type controller and a linear boundary control system in factor form on an infinite-dimensional Hilbert state space H previ- ously introduced by the authors (Grabowski and Callier, 1999). It is assumed for the latter that (a) the observation functional is infinite-time admissible, (b) the factor control vector satisfies a compatibility condition, and (c) the trans- fer function belongs to H∞ (Π+ ) and satisfies a frequency-domain inequality of the circle criterion type. We also require that the closed-loop system be well- posed, i.e. for any initial state x0 ∈ H the truncated input and output sig- nals uT , yT belong to L2 (0, T ) for any T > 0. The technique of the proof adapts Desoer-Vidyasagar’s circle criterion method (Desoer and Vidyasagar, 1975, Ch. 3, Secs. 1 and 2, pp. 37–43, Ch. 5, Sec. 2, pp. 139–142 and Ch. 6, Secs. 3 and 4, pp. 172–174), and uses the input-output map developed by the authors (Grabowski and Callier, 2001). The results are illustrated by two trans- mission line examples: (a) that of the loaded distortionless RLCG type, and (b) that of the unloaded RC type. The conclusion contains a discussion on improving the results by the loop-transformation technique.
Rocznik
Tom
11
Numer
6
Strony
1387-1403
Opis fizyczny
Daty
wydano
2001
Twórcy
  • Institute of Automatics, Academy of Mining and Metallurgy, al. Mickiewicza 30/B1, 30-059 Kraków, Poland
  • University of Namur (FUNDP), Department of Mathematics, Rempart de la Vierge 8, B-5000 Namur, Belgium
Bibliografia
  • Bucci F. (1999): Stability of holomorphic semigroup systems under boundary perturbations, In: Optimal Control of Partial Differential Equations (K.-H. Hoffmann, G. Leugering and F. Tröltzsch, Eds.). — Proc. IFIP WG 7.2 Int. Conf., Chemnitz, Germany, 20–25 April, 1998, ISNM Series, Vol.133, Basel: Birkhäuser, pp.63–76.
  • Bucci F. (2000): Frequency domain stability of nonlinear feedback systems with unbounded input operator. — Dyn. Cont. Discr. Impuls. Syst., Vol.7, No.3, pp.351–368.
  • Desoer C.A. and Vidyasagar M. (1975): Feedback Systems: Input-Output Properties. — New York: Academic Press.
  • Duren P. (1970): Theory of Hp Spaces. — New York: Academic Press.
  • Górecki H., Fuksa S., Grabowski P. and Korytowski A. (1989): Analysis and Synthesis of Time-Delay Systems. — Chichester: Wiley.
  • Grabowski P. (1990): On the spectral – Lyapunov approach to parametric optimization of distributed parameter systems. — IMA J. Math. Contr. Inf., Vol.7, No.4, pp.317–338.
  • Grabowski P. (1994): The LQ controller problem: An example. — IMA J. Math. Contr. Inf., Vol.11, No.4, pp.355–368.
  • Grabowski P. and Callier F.M. (1999): Admissible observation operators. Duality of observation and control using factorizations. — Dyn. Cont., Discr. Impuls. Syst., Vol.6, pp.87– 119.
  • Grabowski P. and Callier F.M. (2000): On the circle criterion for boundary control systems in factor form: Lyapunov approach — Facultés Universitaires Notre–Dame de la Paix a Namur, Publications du Département de Mathématique, Research Report 00–07, Namur, Belgium: FUNDP. Submitted to Int. Eqns. Oper. Theory.
  • Grabowski P. and Callier F.M. (2001): Boundary control systems in factor form: Transfer functions and input-output maps — Int. Eqns. Oper. Theory, Vol.41, pp.1–37.
  • Logemann H. (1991): Circle criterion, small-gain conditions and internal stability for infinite-dimensional systems. — Automatica, Vol.27, No.4, pp.677–690.
  • Logemann H. and Curtain R.F. (2000): Absolute stability results for well-posed infinite- dimensional systems with low-gain integral control. — ESAIM: Contr. Optim. Calc. Var., Vol.5, pp.395–424.
  • Pazy A. (1993): Semigroups of Linear Operators and Applications to PDEs. — Berlin: Springer.
  • Vidyasagar M. (1993): Nonlinear Systems Analysis, 2nd Ed. — Englewood Cliffs NJ: Prentice-Hall.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-amcv11i6p1387bwm
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.