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2001 | 11 | 1 | 7-33
Tytuł artykułu

Well-posed linear systems - a survey with emphasis on conservative systems

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We survey the literature on well-posed linear systems, which has been an area of rapid development in recent years. We examine the particular subclass of conservative systems and its connections to scattering theory. We study some transformations of well-posed systems, namely duality and time-flow inversion, and their effect on the transfer function and the generating operators. We describe a simple way to generate conservative systems via a second-order differential equation in a Hilbert space. We give results about the stability, controllability and observability of such conservative systems and illustrate these with a system modeling a controlled beam.
Rocznik
Tom
11
Numer
1
Strony
7-33
Opis fizyczny
Daty
wydano
2001
otrzymano
2000-09-01
poprawiono
2001-01-01
Twórcy
autor
  • Department of Electrical and Electronic Engineering, Imperial College of Science and Technology, Exhibition Road, London SW7 2BT, United Kingdom
  • Department of Mathematics, Abo Akademi University, FIN-20500 Abo, Finland
  • Department of Mathematics, University of Nancy-I, POB 239, Vandoeuvre les Nancy 54506, France
Bibliografia
  • Adamajan A. and Arov D.Z. (1970): On unitary couplings of semiunitary operators, In: Eleven Papers in Analysis, Vol.95 of American Math. Soc. Transl. - Providence:AMS, pp.75-129.
  • Ammari K., Liu Z. and Tucsnak M. (1999): Decay rates for a beam with pointwise force and moment feedback. - Nancy, preprint.
  • Arov D.Z. and Nudelman M.A. (1996): Passive linear stationary dynamical scattering systems with continuous time.- Int. Eqns. Operat. Theory, Vol.24, pp.1-45.
  • Arov D.Z. (1999): Passive linear systems and scattering theory, In: Dynamical Systems, Control, Coding, Computer Vision (G. Picci and D. Gilliam, Eds.). - Birkhauser, Basel,pp.27-44,
  • Brodskiu i M.S. (1978): Unitary operator colligations and their characteristic functions. - Russian Math. Surveys, Vol.33, No.4, pp.159-191.
  • de Branges L. and Rovnyak J. (1966): Square Summable Power Series. - New York: Holt, Rinehart and Winston.
  • Crawley E.F. and Anderson E.H. (1989): Detailed models forpiezoceramic actuation of beams. - Proc. AIAA Conf., pp.471-476.
  • Destuynder Ph., Legrain I., Castel L. and Richard N.(1992): Theoretical, numerical and experimental discussion of the use of piezoelectric devices for control-structure interaction. - Eur. J. Mech., ASolids, Vol.11, pp.181-213.
  • Helton J.W. (1976): Systems with infinite-dimensional state space: The Hilbert space approach. - Proc. IEEE, Vol.64, pp.145-160.
  • Hille E. and Phillips R.S. (1957): Functional Analysis and Semi-Groups, Rev. Ed. - Providence: AMS.
  • Jaffard S. and Tucsnak M. (1997): Regularity of plate equations with control concentrated in interior curves. - Proc. Roy. Soc. Edinburgh Sect. A, Vol.127, pp.1005-1025.
  • Lax P.D. and Phillips R.S. (1967): Scattering Theory. - New York: Academic Press.
  • Lax P.D. and Phillips R.S. (1973): Scattering theory for dissipative hyperbolic systems. - J. Funct. Anal.,Vol.14, pp.172-235.
  • Livv sic M.S. (173): Operators, Oscillations, Waves (Open Systems). - Transl. Math. Monographs, Vol. 34, Providence: AMS.
  • Ober R. and Montgomery-Smith S. (1990): Bilinear transformation of infinite-dim-ensional state-space systems and balanced realizations of nonrational transfer functions. - SIAM J. Contr. Optim., Vol.28, pp.438-465.
  • Ober R. and Wu Y. (1996): Infinite-dimensional continuous-time linear systems: stability and structure analysis.- SIAM J. Contr. Optim., Vol.34, pp.757-812.
  • Salamon D. (1987): Infinite dimensional linear systems with unbounded control and observation: A functional analytic approach. - Trans. Amer. Math. Soc., Vol.300, pp.383-431.
  • Salamon D. (1989): Realization theory in Hilbert space. - Math. Syst. Theory, Vol.21, pp.147-164.
  • Staffans O.J. (1997): Quadratic optimal control of stable well-posed linear systems. - Trans. Amer. Math. Soc.,Vol.349, pp.3679-3715.
  • Staffans O.J. (1998a): Coprime factorizations and well-posed linear systems. - SIAM J. Contr. Optim., Vol.36, pp.1268-1292.
  • Staffans O.J. (1998b): On the distributed stable full information H^∞ minimax problem. - Int. J. Robust Nonlin. Contr., Vol.8, pp.1255-1305.
  • Staffans O.J. (1998c): Quadratic optimal control of well-posed linear systems. - SIAM J. Contr. Optim.,Vol.37, pp.131-164.
  • Staffans O.J. (1999): Lax-Phillips scattering and well-posed linear systems. - Proc. 7th IEEE Mediterranean Conf. Control and Systems, Haifa, Israel, published on CD-ROM.
  • Staffans O.J. (2001): Well-Posed Linear Systems. - Book in preparation.
  • Staffans O.J. and Weiss G. (2001a): Transfer functions of regular linear systems. Part II: The system operator and the Lax-Phillips semigroup. - London: preprint.
  • Staffans O.J. and Weiss G. (2001b): Transfer functions of regular linear systems. Part III: Inversions and duality. - London: preprint.
  • Sz.-Nagy B. and Foiacs C. (1970): Harmonic Analysis of Operators on Hilbert Space. - Amsterdam and London: North-Holland.
  • Tucsnak M. and Weiss G. (2001): How to get a conservative well-posed linear system out of thin air. - London: preprint.
  • Weiss G. (1989a): Admissible observation operators for linear semigroups. - Israel J. Math., Vol.65, pp.17-43.
  • Weiss G. (1989b): Admissibility of unbounded control operators. - SIAM J. Contr. Optim., Vol.27, pp.527-545.
  • Weiss G. (1989c): The representation of regular linear systems on Hilbert spaces, In: Control and Optimization of Distributed Parameter Systems (F. Kappel, K. Kunisch, W. Schappacher, Eds.).- Basel: Birkhuser Verlag, pp.401-416.
  • Weiss G. (1994a): Regular linear systems with feedback. - Math. Contr. Signals Syst., Vol.7, pp.23-57.
  • Weiss G. (1994b): Transfer functions of regular linear systems. Part I: Characterizations of regularity. - Trans. Amer. Math. Soc., Vol.342, pp.827-854.
  • Weiss G. (1999): A powerful generalization of the Carleson measure theorem?, In: Open Problems in Mathematical Systems and Control Theory (V. Blondel, E. Sontag, M. Vidyasagar and J. Willems, Eds.). - London: Springer-Verlag, pp.267-272.
  • Weiss M. and Weiss G. (1997): Optimal control of stable weakly regular linear systems. - Math. Contr. Signals Syst., Vol.10, pp.287-330.
  • Yamamoto Y. (1981): Realization theory of infinite-dimensionallinear systems, Parts I and II. - Math. Syst. Theory, Vol.15, pp.55-77, pp.169-190.
Typ dokumentu
Bibliografia
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