Multivariable linear, time invariant control system design invariably involves loop shaping. When it is necessary to shape several time and frequency responses simultaneously and keep gains within prescribed bounds, classical design techniques become overpowered. Fortunately, at this point the designer can call upon semi-infinite optimization (see [Pol.3]) which is a natural tool for solving control system design problems that require squeezing time and frequency responses into preassigned tubes, as well as for taking plant uncertainty into account. Semi-infinite optimization can also be used to carry out trade-offs when all the design requirements cannot be satisfied at the same time. The use of semi-infinite optimization in control system design is most successful when carried out in an interactive computing environment.
E. Polak, E. Polak,
"Optimization-Based Computer-Aided Design Of Control Systems: A Survey", Proc. SPIE 0857, IECON'87:Automated Design and Manufacturing, (19 October 1987); doi: 10.1117/12.943264; https://doi.org/10.1117/12.943264