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$\cal H_\infty$ control state feedback and Rayleigh quotient. (English)
Comput. Methods Appl. Mech. Eng. 191, No.3-5, 489-501 (2001).
The paper is an attempt to apply some results from structural mechanics in robust control design based on an $H_\infty$ approach. The authors find the analogy between the value of the optimal bounding parameter in $H_\infty$ control and the smallest eigenvalue of a generalized Rayleigh quotient which can be computed to any required precision. The authors propose to use the precise integrative method and the corresponding extended algorithm of {\it W. H. Wittrick} and {\it F. W. Williams} [Q. J. Mech. Appl. Math. 24, 263-284 (1971; Zbl 0227.73022)] for this purpose. Some examples indicating the accuracy of the proposed technique are also presented.
Reviewer: A.Šwierniak (Gliwice)