Theory of LTR for nonminimum phase systems, recoverable target loops, recovery in a subspace. I. Analysis

A complete analysis of the loop transfer recovery (LTR) problem using full order observer-based controllers for general systems that are not necessarily left invertible and minimum phase is considered. The analysis focuses on three fundamental issues. The first is concerned with what can and cannot be achieved for a given system and for an arbitrarily specified target loop transfer function. The second is concerned with the development of necessary and/or sufficient conditions for a target loop to be either exactly or asymptotically recovered for a given system. The third issue deals with the development of method(s) to test whether recovery is possible in a given subspace of the control space. Such an analysis pinpoints the limitations of the given system for the recovery of arbitrarily specified target loops by observer-based controllers. Furthermore, the analysis discovers a multitude of ways to shape the loops as closely as possible to the target shapes. Also, possible pole-zero cancellations between the eigenvalues of the controller and the input and/or output decoupling zeros of the plant are characterized