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2001 | 11 | 6 | 1261-1276
Tytuł artykułu

Szegő's first limit theorem in terms of a realization of a continuous-time time-varying systems

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
It is shown that the limit in an abstract version of Szegő's limit theorem can be expressed in terms of the antistable dynamics of the system. When the system dynamics are regular, it is shown that the limit equals the difference between the antistable Lyapunov exponents of the system and those of its inverse. In the general case, the elements of the dichotomy spectrum give lower and upper bounds.
Rocznik
Tom
11
Numer
6
Strony
1261-1276
Opis fizyczny
Daty
wydano
2001
Twórcy
  • Department of Electrical and Computer Engineering, The Johns Hopkins University, MD 21218, Baltimore, U.S.A.
  • Department of Electrical and Computer Engineering, The Johns Hopkins University, MD 21218, Baltimore, U.S.A.
Bibliografia
  • Ahiezer N.I. (1964): A functional analogue of some theorems on Toeplitz matrices. — Ukrain. Mat. Ž., Vol.16, pp.445–462. English Transl. (1966): Amer. Math. Soc. Transl., Vol.50, pp.295–316.
  • Arnold L. (1998): Random Dynamical Systems. — Berlin: Springer.
  • Böttcher A. and Silbermann B. (1999): Introduction to Large Truncated Toeplitz Matrices. — New York: Springer.
  • Coppel W.A. (1978): Dichotomies in Stability Theory. — Berlin: Springer.
  • Dieci L., Russell R.D. and van Vleck E.S. (1997): On the computation of Lyapunov exponents for continuous dynamical systems. — SIAM J. Numer. Anal., Vol.34, No.1, pp.402–423.
  • Dym H. and Ta’assan S. (1981): An abstract version of a limit theorem of Szegő. — J. o Funct. Anal., Vol.43, No.3, pp.294–312.
  • Gohberg I. and Kreĭn M.G. (1969): Introduction to the Theory of Linear, Nonselfadjoint Operators. — Providence, RI: AMS.
  • Gohberg I., Kaashoek M.A. and van Schagen F. (1987): Szegő-Kac-Achiezer formulas in terms of realizations of the symbol. — J. Funct. Anal., Vol.74, No.1, pp.24–51.
  • Grenander U. and Szegő G. (1958): Toeplitz Forms and Their Applications. — Berkeley: University of California.
  • Iglesias P.A. (2001): A time-varying analogue of Jensen’s formula. — Int. Eqns. Oper. Theory, Vol.40, No.1, pp.34–51.
  • Iglesias P.A. (2002): Logarithmic integrals and system dynamics: An analogue of Bode’s sensitivity integral for continuous-time, time-varying systems. — Lin. Alg. Appl., Vol.343– 344, pp.451–471.
  • Ilchmann A. and Kern G. (1987): Stabilizability of systems with exponential dichotomy. — Syst. Contr. Lett., Vol.8, No.3, pp.211–220.
  • Kac M. (1954): Toeplitz matrices, translation kernels and a related problem in probability theory. — Duke Math. J., Vol.21, pp.501–509.
  • Kalman R.E. (1960): Contributions to the theory of optimal control. — Boletín de la Sociedad Matemática Mexicana, Vol.5, No.2, pp.102–119.
  • Millionščikov V.M. (1969): A proof of the existence of nonregular systems of linear differential equations with quasiperiodic coefficients. — Differencial’nye Uravnenija, Vol.5, pp.1979–1983.
  • Ravi R., Nagpal K.M. and Khargonekar P.P. (1991): H∞ control of linear time-varying systems: A state-space approach. — SIAM J. Contr. Optim., Vol.29, No.6, pp.1394– 1413.
  • Rugh W.J. (1996): Linear System Theory, 2nd Ed. — Englewood Cliffs, NJ: Prentice-Hall.
  • Sacker R.J. and Sell G.R. (1978): A spectral theory for linear differential systems. — J. Diff. Eqns., Vol.27, No.3, pp.320–358.
  • Vojtenko S.S. (1987): Existence conditions for stabilizing and antistabilizing solutions to the nonautonomous matrix Riccati differential equation. — Kybernetika, Vol.23, No.1, pp.32–43.
  • Zhou K., Doyle J.C. and Glover K. (1996): Robust and Optimal Control. — Upper Saddle River, NJ: Prentice-Hall.
Typ dokumentu
Bibliografia
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