Loop transfer recovery with an H∞ optimality criterion

A formulation of the Loop Transfer Recovery (LTR) design problem using an ξ_∞ (sub-) optimality criterion is presented in this paper and state space formulae are given as its solution. The LTR problem is formulated as an ξ_∞ norm constraint for a recovery error which can be defined in two ways: either as a recovery error of the sensitivity function or as a recovery error of the input-output transfer function. Applying output feedback controllers we proceed from the recovery errors to an ξ_∞ state space formulation. The control problems corresponding to the two recovery error types are given as two different ξ_∞ state space problems. Each ξ_∞ problem is decomposed into the well known regular problem and a totally singular problem. The dynamics of the obtained controllers are at most of order 2n. Moreover, the ξ_∞/LTR method handles both minimum phase as well as non minimum phase systems in a common framework.