Hisaya Fujioka, Yuji Wakasa, Yutaka Yamamoto
2000 Journal of the Operations Research Society of Japan  
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 approach
more » ... odern approach using mathernatical programming such a/ LMIs and BMIs. Twe types of glebal optimization algorithms to solve BMIs are introdllced. The OpeiationsReseaich Society of Japan Ciptimization in Control Spistetn Design 49 This stability problem captured the interest of Sir Maxwell, and he wrote perhaps the first paper on the theory of control: "On Governors" I28]. He could derive stability conditions for systems with order less than or equal to 3, but no more, The general case was later resolved independently by Routh and Hurwitz. Great progress has been made since then. The notion of frequency response was found and The OpeiationsReseaichSociety of Japan 70 E Fbjioka.M PVlakasn & ilYhn]amoto
doi:10.15807/jorsj.43.48 fatcat:mnfhnbxqybahdfb53swfegmkqm