区間プラントを含むルーリエ系に対するポポフの定理の適用について

抄録

Lur'e problems are historical ones dating back to the 60's, where uncertainties were taken into account only in nonlinear parts. In recent years, however, some new aspects are brought into the problems by taking uncertainties in linear parts as well, into consideration. A possible way to express these uncertainties in input-output relations is to use interval plants described by ratios of two interval polynomials. It is revealed recently that in order to guarantee absolute stability of a Lur'e system with an interval plant using the circle criterion, checking the condition of the criterion for only 16 extreme plants suffices.
In this paper, we attempt to prove a parallel result for the Popov criterion. We show that the condition of Popov's theorem for the entire interval plant can be met by checking only 16 extreme plants. A numerical example is presented to illustrate the result.