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Quantitative Lp stability analysis of a class of linear time-varying feedback systems

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Języki publikacji
EN
Abstrakty
EN
The Lp stability of linear feedback systems with a single time-varying sector-bounded element is considered. A sufficient condition for Lp stability, with 1LpL Y, 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
Strony
179--184
Opis fizyczny
Bibliogr. 11 poz., rys.
Twórcy
autor
  • Department of Mechanical and Aerospace Engineering Princeton University, Princeton, NJ 08544, U.S.A., pgurfil@princeton.edu
Bibliografia
  • [1] Desoer C.A. and Vidyasagar M. (1975): Feedback Systems: Input-Output Properties. — New York: Academic Press.
  • [2] Doyle J.C., Francis B.A. and Tannenbaum A.R. (1992): Feedback Control Theory. — New York: Macmillan Publishing.
  • [3] 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.
  • [4] Mossaheb S. (1982): The circle criterion and the LP stability of feedback systems. — SIAM J. Contr. Optim., Vol. 20, No. 1, pp. 144–151.
  • [5] 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.
  • [6] 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.
  • [7] 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.
  • [8] Shinar J. (1976): Divergence range of homing missiles.—Israel J. Technol., Vol. 14, pp. 47–55.
  • [9] Vidyasagar M. (19): Nonlinear Systems Analysis, 2nd Ed.. — New Jersey: Upper Saddle River.
  • [10] Zames G. (1990): On input-output stability of time-varying nonlinear feedback systems-Part II: Conditions involving circles in the frequency plane and sector nonlinearities. — IEEE Trans. Automat. Contr., Vol. AC–11, No. 2, pp. 465–476.
  • [11] Zarchan P. (1990): Tactical and Strategic Missile Guidance. — Washington: AIAA.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BPZ1-0002-0016
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