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2003 | 13 | 2 | 179-184
Tytuł artykułu

Quantitative L^{P} stability analysis of a class of linear time-varying feedback systems

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
The L^{P} stability of linear feedback systems with a single time-varying sector-bounded element is considered. A sufficient condition for L^{P} stability, with 1 ≤ p ≤ ∞, is obtained by utilizing the well-known small gain theorem. Based on the stability measure provided by this theorem, quantitative results that describe output-to-input relations are obtained. It is proved that if the linear time-invariant part of the system belongs to the class of proper positive real transfer functions with a single pole at the origin, the upper bound on the output-to-input ratio is constant. Thus, an explicit closed-form calculation of this bound for some simple particular case provides a powerful generalization for the more complex cases. The importance of the results is illustrated by an example taken from missile guidance theory.
Rocznik
Tom
13
Numer
2
Strony
179-184
Opis fizyczny
Daty
wydano
2003
otrzymano
2002-08-10
poprawiono
2002-10-16
Twórcy
autor
  • Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, NJ 08544, U.S.A.
Bibliografia
  • Desoer C.A. and Vidyasagar M. (1975): Feedback Systems: Input-Output Properties. - New York: Academic Press.
  • Doyle J.C., Francis B.A. and Tannenbaum A.R. (1992): Feedback ControlTheory. - New York: Macmillan Publishing.
  • Gurfil P., Jodorkovsky M. and Guelman M. (1998): Finite time stability approach to proportional navigation systems analysis. - J. Guid. Contr. Dynam., Vol. 21, No. 6, pp. 853-861.
  • Mossaheb S. (1982): The circle criterion and the L^P stability of feedback systems. - SIAM J. Contr. Optim., Vol. 20, No. 1, pp. 144-151.
  • Sandberg I.W. (1964): A frequency domain condition for the stability of feedback systems containing a single time-varying nonlinear element.- Bell Syst. Tech. J., Vol. 43, pp. 1601-1608.
  • Sandberg I.W. (1965): Some results on the theory of physical systems governed by nonlinear functional equations. - Bell Syst. Tech. J., Vol. 44, No. 5, pp. 871-898.
  • Sandberg I.W. and Johnson K.K. (1990): Steady state errors and the circle criterion. - IEEE Trans. Automat. Contr., Vol. 35, No. 1, pp. 530-534.
  • Shinar J. (1976): Divergence range of homing missiles. - Israel J. Technol., Vol. 14, pp. 47-55.
  • Vidyasagar M. (19): Nonlinear Systems Analysis, 2nd Ed.. -New Jersey: Upper Saddle River.
  • Zames G. (1990): On input-output stability of time-varying nonlinear feedback systems-Part II: Conditions involving circles in the frequency planeand sector nonlinearities. - IEEE Trans. Automat. Contr., Vol. AC-11, No. 2, pp. 465-476.
  • Zarchan P. (1990): Tactical and Strategic Missile Guidance. -Washington: AIAA.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-amcv13i2p179bwm
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