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An analysis of \(H^{\infty}\)-optimization design methods. (English) Zbl 0592.93015

For several years, \(H^{\infty}\)-optimization has received considerable attention as a design method for linear feedback systems. The purpose of this paper is to analyze one particular \(H^{\infty}\)-optimization problem with respect to its efficacy in coping with certain design limitations. The problem analyzed is that of minimizing the weighted infinity norm of the sensitivity function of a scalar linear time- invariant feedback system, and the design limitation is a tradeoff imposed by the plant having nonminimum-phase zeros. Two issues are raised. One is the ease with which the \(H^{\infty}\)-methodology allows the tradeoff to be manipulated in design. The other is the issue of compensator stability when the plant has more than one nonminimum phase zero. In each case, it seems that further details need to be addressed by the emerging design theory, which is in general promising. Although it may be argued that the problem analyzed in this paper is too simplistic to be of interest, the issues raised also appear in more general \(H^{\infty}\)-optimization problems where they are less amenable to analysis.

MSC:

93B35 Sensitivity (robustness)
30D55 \(H^p\)-classes (MSC2000)
93C05 Linear systems in control theory
93B55 Pole and zero placement problems
93B50 Synthesis problems
93C99 Model systems in control theory
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