Loop Transfer Recovery (LTR) is part of the Communications and Control Engineering Series (CCES) edited by Professors B.W. Dickinson, E.D. Sontag, M. Thoma, A. Fettweis, J.L. Massey and J.W. Modestino. Loop Transfer Recovery deals with several issues of analysis and design of the Loop Transfer Recovery (LTR) problem. It discusses when and how an LTR is possible and outlines different controller structures and the available design freedom. An explanation of the actual design methods for accomplishing an LTR is given. Besides dealing with observer based measurement feedback controllers, which are commonly used for LTR, a new controller with a different architecture which out performs observer based controllers is presented. This publication will be of benefit to anyone who has completed a first graduate course in linear systems and state-space methods, together with an elementary knowledge of Linear Quadratic Control.

Table of Contents:
1 Introduction.- 1.1 Introduction.- 1.2 Problem formulation.- 1.3 Preliminaries.- 2 Preliminary Analysis of Continuous LTR.- 2.1 Introduction.- 2.2 Preliminary analysis.- 2.2.1 Luenberger observer based controller.- 2.2.2 Full order observer based controller.- 2.2.3 Reduced order observer based controller.- 2.2.4 Relationship between the recovery matrices Mf(s) and Mr(s).- 2.A Proof of Lemma 2.2.1.- 2.B Proof of Proposition 2.2.2.- 3 Continuous LTR - Detailed Analysis.- 3.1 Introduction.- 3.2 Recovery analysis while not using the knowledge of F.- 3.3 Analysis for recoverable target loop transfer functions.- 3.4 Recovery analysis in a given subspace.- 3.5 Duality of LTRI and LTRO.- 3.A Proof of Lemma 3.2.1.- 3.B Proof of Lemma 3.2.2.- 3.C Proof of Proposition 3.2.2.- 3.D Proof of Lemma 3.2.3.- 3.E Proof of Corollary 3.3.2.- 3.F Proof of Lemma 3.4.2.- 3.G Proof of Lemma 3.4.3.- 4 Continuous LTR - Design.- 4.1 Introduction.- 4.2 Design constraints and the available freedom.- 4.3 ATEA design method.- 4.3.1 General ATEA design.- 4.3.2 Design for exactly recoverable target loop transfer functions.- 4.4 Optimization based design methods.- 4.4.1 H2-optimization based design algorithms.- 4.4.2 H?-optimization based design algorithms.- 4.5 Design for recovery over a specified subspace.- 4.6 LTR design for output break point.- 4.7 Comparison of ATEA and optimization based design algorithms.- 4.A Proof of Theorem 4.3.1.- 4.B Proof of Theorem 4.3.2.- 4.C Proof of Theorem 4.4.2.- 5 Introduction to Discrete LTR.- 5.1 Introduction.- 5.2 Problem formulation.- 5.3 Preliminaries.- 6 Preliminary Analysis of Discrete LTR.- 6.1 Introduction.- 6.2 Controller structures for discrete LTR.- 6.2.1 Luenberger estimator based controller.- 6.2.2 Prediction estimator based controller.- 6.2.3 Current estimator based controller.- 6.2.4 Reduced order estimator based controller.- 6.3 Preliminary analysis.- 6.A Proof of Proposition 6.3.1.- 7 Discrete LTR - Detailed Analysis.- 7.1 Introduction.- 7.2 Recovery analysis while not using the knowledge of F.- 7.3 Analysis for recoverable target loop transfer functions.- 7.4 Recovery analysis in a given subspace.- 7.5 Duality of LTRI and LTRO.- 7.A Proof of Lemma 7.2.2.- 7.B Proof of Corollary 7.3.1.- 7.C Proof of Theorem 7.4.4.- 8 Discrete LTR - Design.- 8.1 Introduction.- 8.2 Design constraints and the available freedom.- 8.3 Design by eigenstructure assignment.- 8.4 Optimization based design methods.- 8.4.1 H?-optimization based algorithm.- 8.4.2 H2-optimization based algorithm.- 8.5 Design for recovery over a specified subspace.- 8.6 LTR design for output break point.- 8.A Proof of Theorem 8.4.1.- 9 Closed-Loop Transfer Recovery.- 9.1 Introduction.- 9.2 Continuous CLTR.- 9.2.1 Problem formulation.- 9.2.2 General analysis.- 9.2.3 Design methods and examples.- 9.3 Discrete CLTR.- 9.3.1 Problem formulation.- 9.3.2 General analysis.- 9.3.3 Design methods and examples.- 9.A Proof of Lemma 9.2.1.- 10 Some Issues of Controller Architecture.- 10.1 Introduction.- 10.2 Recoverability with an arbitrarily structured controller.- 10.3 CSS architecture based controllers for LTR.- 10.3.1 Full order CSS architecture based controller.- 10.3.2 Reduced order CSS architecture based controller.- 10.3.3 Properties of the CSS architecture based controllers.- 10.4 Design examples.- 10.5 Open research problems.- 10.A Proof of Theorem 10 2 1.- 10.B Proof of Lemma 10.3.1.- 10.C Proof of Theorem 10 3 1.