Quantitative L^p stability analysis of a class of linear time-varying feedback systems

• Autorzy: Gurfil P.
• 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.

Słowa kluczowe

EN

Lp stability; time-varying Lur'e systems; functional analysis

PL

stabilność Lp; system zmienny w czasie; analiza funkcjonalna

• Wydawca: Oficyna Wydawnicza Uniwersytetu Zielonogórskiego
• Czasopismo: International Journal of Applied Mathematics and Computer Science
• Rocznik: 2003
• Tom: Vol. 13, no 2
• Strony: 179--184
• Opis fizyczny: Bibliogr. 11 poz., rys.

Twórcy

autor

Gurfil P.

• Department of Mechanical and Aerospace Engineering Princeton University, Princeton, NJ 08544, U.S.A.,

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.