An internal state decomposition approach to a discrete-time H2H2 control problem with irrational input non-minimum phase property

An internal state decomposition approach to a class of discrete-time H2H2 control problems with irrational non-minimum phase property at the control input is proposed. This is a generalization of the state-variable transformation to derive the discrete-time Smith predictor for a single input-delay system. The H2H2 optimal controller is derived using the orthogonality principle in H2H2 space as a direct consequence of the state decomposition. The characterization of the optimal cost by the previous and alternative truncation operators is also discussed.