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An introduction to a nonlinear programming approach to optimal continuous robust parametric H2 control

A parametric H2 optimal control problem for linear continuous time-invariant systems is discussed. The control setup allows that any matrix coefficient of a system state space description be subjected to parameter uncertainties. Controllers with any order and any structure can be synthesized by recasting it as a Static Output Feedback problem. A modified H2 cost functional that allows to start the optimization with a non stabilizing controller is used. First and second order derivatives for the modified H2 cost functional with respect to system uncertainties and controller parameters are given. Based on this setup, several parametric robust design problems are formulated.