Book description
This book introduces the socalled "stable factorization approach" to the synthesis of feedback controllers for linear control systems. The key to this approach is to view the multiinput, multioutput (MIMO) plant for which one wishes to design a controller as a matrix over the fraction field F associated with a commutative ring with identity, denoted by R, which also has no divisors of zero. In this setting, the set of singleinput, singleoutput (SISO) stable control systems is precisely the ring R, while the set of stable MIMO control systems is the set of matrices whose elements all belong to R. The set of unstable, meaning not necessarily stable, control systems is then taken to be the field of fractions F associated with R in the SISO case, and the set of matrices with elements in F in the MIMO case. The central notion introduced in the book is that, in most situations of practical interest, every matrix P whose elements belong to F can be "factored" as a "ratio" of two matrices N,D whose elements belong to R, in such a way that N,D are coprime. In the familiar case where the ring R corresponds to the set of boundedinput, boundedoutput (BIBO)stable rational transfer functions, coprimeness is equivalent to two functions not having any common zeros in the closed right halfplane including infinity. However, the notion of coprimeness extends readily to discretetime systems, distributedparameter systems in both the continuous as well as discretetime domains, and to multidimensional systems. Thus the stable factorization approach enables one to capture all these situations within a common framework. The key result in the stable factorization approach is the parametrization of all controllers that stabilize a given plant. It is shown that the set of all stabilizing controllers can be parametrized by a single parameter R, whose elements all belong to R. Moreover, every transfer matrix in the closedloop system is an affine function of the design parameter R. Thus problems of reliable stabilization, disturbance rejection, robust stabilization etc. can all be formulated in terms of choosing an appropriate R. This is a reprint of the book Control System Synthesis: A Factorization Approach originally published by M.I.T. Press in 1985.Table of contents
 Preface
 Preface for the Original Edition

Filtering and Sensitivity Minimization
 Problem Statement
 Some Facts about Hardy Spaces (1/2)
 Some Facts about Hardy Spaces (2/2)
 Filtering
 Sensitivity Minimization: Scalar Case (1/2)
 Sensitivity Minimization: Scalar Case (2/2)
 Sensitivity Minimization: Fat Plant Case (1/4)
 Sensitivity Minimization: Fat Plant Case (2/4)
 Sensitivity Minimization: Fat Plant Case (3/4)
 Sensitivity Minimization: Fat Plant Case (4/4)
 Sensitivity Minimization: General Case (1/2)
 Sensitivity Minimization: General Case (2/2)
 TwoParameter Compensator (1/2)
 TwoParameter Compensator (2/2)

Robustness
 Introduction
 Graph Topology (1/4)
 Graph Topology (2/4)
 Graph Topology (3/4)
 Graph Topology (4/4)
 Graph Metric (1/2)
 Graph Metric (2/2)
 Robustness Conditions (1/4)
 Robustness Conditions (2/4)
 Robustness Conditions (3/4)
 Robustness Conditions (4/4)
 Robust and Optimal Regulation (1/4)
 Robust and Optimal Regulation (2/4)
 Robust and Optimal Regulation (3/4)
 Robust and Optimal Regulation (4/4)
 Genericity (1/2)
 Genericity (2/2)
 Extensions to General Settings
 Algebraic Preliminaries
 Preliminaries on Matrix Rings
 Topological Preliminaries
 Bibliography (1/2)
 Bibliography (2/2)
 Author's Biography
 Index
Product information
 Title: Control System Synthesis
 Author(s):
 Release date: June 2011
 Publisher(s): Morgan & Claypool Publishers
 ISBN: 9781608456635
You might also like
book
Codeless Data Structures and Algorithms : Learn DSA Without Writing a Single Line of Code
In the era of selftaught developers and programmers, essential topics in the industry are frequently learned …
book
Unit Testing Principles, Practices, and Patterns
Unit Testing Principles, Patterns and Practices teaches you to design and write tests that target the …
book
Learning Python, 5th Edition
Get a comprehensive, indepth introduction to the core Python language with this handson book. Based on …
book
Process Control Design for Industrial Applications
This book presents the most important methods used for the design of digital controls implemented in …