A Historical Survey
In this chapter we give an informal discussion of the history of the problem of absolute stability from the early formulation by Lurye to the recent development of the method of the integral-quadratic constraints. The important milestones were the resolving equations of Lurye, the Popov criterion, and the Kalman-Yakubovich Lemma. The discussion of the Popov criterion includes its recent application to the Aizerman problem for retarded systems. We also discuss the most important developments of the 1960s and 1970s, especially the so-called stability (or Zames-Falb) multipliers. The chapter concludes with a discussion of some historical applications of the absolute stability analysis.
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