State-space solutions to the ℋ∞/LTR design problem

The LTR design problem using an ℋ∞ optimality criterion is presented for two types of recovery errors, the sensitivity recovery error and the input-output recovery error. For both errors two different approaches are presented. First, following the classical LTR design philosophy, a Luenberger observer based approach is proposed, where the ℋ∞ part of the controller is appended to a standard full-order observer. Second, allowing for general controllers, an ℋ∞ state-space problem is formulated directly from the recovery errors. Both approaches lead to controller orders of at most 2n. In the minimum phase case, though, the order of the controllers can be reduced to n in all cases. The control problems corresponding to the various controller types are given as four different singular ℋ∞ state-space problems, and the solutions are given in terms of the relevant equations and inequalities.