Necessary and sufficient conditions under which a discrete time h 2-Optimal control problem has an unique solution

Abstract

A set of necessary and sufficient conditions under which a general discrete timeH2-optimal control problem has a unique solution is derived. It is shown that the solution for a discrete time H2-optimal control problem,if it exists,is unique if and only if i) the transfer function from the control input to the controlled output is left invertible, and ii) the transfer function from the disturbance to the measurement output is right invertible.