Polynomial matrix solution to the standard H₂ optimal control problem

Abstract

A solution to the ‘standard’ H ₂ optimal control problem is presented. The solution is derived in both traditional Wiener transfer function form and in the more recent polynomial matrix form. The general formulation enables coloured measurement noise and dynamic cost weightings to be included in the system description. The results also apply when single or two degrees of freedom controller structures are employed. The feedforward control problem can also be represented within the general framework considered.