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This paper reviews i) the background for the modern ffOe control theory, and then ii) how it led to t-he modern optirnization theory such as those using LMIs (linear matrix inequalities) and BMIs (bilinear matrix inequalities). Starting from the simplest sensitivity minimization problem, we giye solutions via the Nevalirma-Pick interpolation and the Nehari theorem. The latter leads to a ruccati equation on which most ofthe llOO solutiens are based. This in turn leads to the modern approachdoi:10.15807/jorsj.43.48 fatcat:mnfhnbxqybahdfb53swfegmkqm