On a problem of analytic design of an optimal controller

This article is devoted to the further development of the technique of analytic design of an optimal controller for the case of functionals with an integrand of the form $x'Qx+x'Pu+u'Ru$. In this case the problems of analytic design are considered both without disturbances and at constantly acting disturbances. The statement of the problem for optimal control of a vibration-protective system (VPS) is given, for the solution of which the technique outlined in the article can be used for the solution of the problem of analytic design of the optimal controller.