Abstract
Consideration was given to the generalizations of the Petersen lemma of matrix uncertainty which is one of the main technical facilities for handling the structured matrix uncertainties used to advantage in various robust formulations of the problems of stabilization and control.
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Petersen, I., A Stabilization Algorithm for a Class of Uncertain Systems, Syst. Control Lett., 1987, vol. 8, pp. 351–357.
Khlebnikov, M.V., Polyak, B.T., and Kuntsevich, V.M., Optimization of Linear Systems Subject to Bounded Exogenous Disturbances: The Invariant Ellipsoid Technique, Autom. Remote Control, 2011, vol. 72, no. 11, pp. 2227–2275.
Khlebnikov, M.V. and Shcherbakov, P.S., Petersen’s Lemma on Matrix Uncertainty and Its Generalization, Autom. Remote Control, 2008, vol. 69, no. 11, pp. 1932–1945.
Shcherbakov, P.S. and Khlebnikov, M.V., New Generalizations of Petersen’s Lemma of Matrix Uncertainty, in Mezhd. konf. “Modelirovanie, upravlenie i ustoichivost’ ” (Int. Conf. “Modeling, Control, and Stability” (MCS-2012)), Sevastopol, Ukraine, September 10–14, 2012, Simferopol: DIAIPI, 2012, p. 110.
Polyak, B.T., Vvedenie v optimizatsiyu, Moscow: Nauka, 1983. Translated into English under the title Introduction to Optimization, New York: Optimization Software, 1987.
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Original Russian Text © M.V. Khlebnikov, 2014, published in Avtomatika i Telemekhanika, 2014, No. 5, pp. 137–142.
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Khlebnikov, M.V. New generalizations of the Petersen lemma. Autom Remote Control 75, 917–921 (2014). https://doi.org/10.1134/S0005117914050099
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DOI: https://doi.org/10.1134/S0005117914050099