A Robust H2 Performance Problem for Uncertain Plants

An optimal control problem with robust performance is studied for plants with linear time-invariant, and possibly structured, uncertainties. The control performance is characterized in a deterministic setting as an average performance with respect to L2-disturbances. For linear time-invariant systems, the average performance measure equals the H2-norm of the system transfer function. The robust control problem consists of minimizing an upper bound on the worst value of the performance measure with respect to the plant uncertainties. The upper bound is introduced in the form of a quadratic cost with quadratic frequency-domain constraints, and an associated dual minimization problem, which consists of minimizing a Lagrangian-type function with respect to a (Lagrange multiplier) weighting lter. The resulting robust control problem involves a standard mixed H2=H1 problem as a subproblem. An optimization-based procedure for the numerical solution of the control problem is given. The proposed controller synthesis procedure is illustrated with a numerical example.