Abstract: An adaptive H.infin. industrial control system has a controller 21 controlling an industrial process 20 (ship, rolling mill, etc.), the state of which is measured (y). The controller and process outputs are fed to a parameter estimator 34 which estimates the operating polynomials (transfer functions or delay operator functions) A, B, and C of the process. A controller design unit 35 processes the output of estimator 34 to produce coefficients for the controller 21, which implements a polynomial ratio C.sub.n /C.sub.d. The H.infin. algorithm is based on minimizing a "square of sum" form of function (P.sub.c .multidot.u(t)+F.sub.c .multidot.e(t)).sup.2, which results in equations which are easier to solve than those arising from the usual "sum of squares" form of function. A polynomialL=P.sub.cn F.sub.cd B-F.sub.cn P.sub.cd Ais calculated, the unstable zeros L.sub.-- are calculated, the matrix equationsFAP.sub.cd .lambda.+L.sub.-- G=P.sub.cn CF*z.sup. -nFBF.sub.cd .lambda.-L.sub.-- H=F.sub.cn CF*z.sup.