Design of H∞ optimal stable stabilizing compensator

The H^∞ control problem by stable compensator is solved for the 1-block case. The optimal closed loop transfer function appears to be the singular inner function in the Hardy class H^∞(C₊). In particular, no rational transfer function of the controller can be optimal in this problem. A nonlinear algebraic system with the equal number of variables and equations is obtained from which the minimum of the H^∞ functional and the parameters of the optimal transfer function can be computed. It is shown how to design a minimizing sequence of rational approximations to this transfer function. Examples illustrate the result