The total synthesis problem of linear multivariable control Part II: Unity feedback and the design morphism

Under broad assumptions, it is known [1] that there is, in general, no "separation principle" to guarantee optimality of a division between control law design and filtering of plant uncertainty. It is possible, however, to develop parameterizations of nominal responses and to examine their capabilities in the feedback situation. In an earlier study, the authors presented a coordinate-free approach [34] to the Nominal Design Problem (NDP), which addresses control action and plant output syntheses, independently of the controller configuration. It was shown that NDP depended only upon plant structural matrices and a single design morphism. This paper studies the role of this design morphism in unity feedback synthesis (UFS). NDP, together with feedback synthesis, is understood as a Total Synthesis Problem.