Book description
A Generalized Framework of Linear Multivariable Control proposes a number of generalized models by using the generalized inverse of matrix, while the usual linear multivariable control theory relies on some regular models.
The book supports that in Hinfinity control, the linear fractional transformation formulation is relying on the inverse of the block matrix. If the block matrix is not regular, the Hinfinity control does not apply any more in the normal framework. Therefore, it is very important to relax those restrictions to generalize the classical notions and models to include some nonregular cases.
This book is ideal for scholars, academics, professional engineer and students who are interested in control system theory.
 Presents a comprehensive set of numerical procedures, algorithms, and examples on how to deal with irregular models
 Provides a summary on generalized framework of linear multivariable control that focuses on generalizations of models and notions
 Introduces a number of generalized models by using the generalized inverse of matrix
Table of contents
 Cover image
 Title page
 Table of Contents
 Copyright
 1: Introduction
 2: Mathematical preliminaries
 3: Generalized inverse of matrix and solution of linear system equation
 4: Polynomial fraction description
 5: Stability
 6: Fundamental approaches to control system analysis
 7: Determination of finite and infinite frequency structure of a rational matrix

8: The solution of a regular PMD and the set of impulsive free initial conditions
 Abstract
 8.1 Introduction
 8.2 Preliminary results
 8.3 A solution for the LNHMDEs
 8.4 The smooth and impulsive solution components and impulsive free initial conditions: C∞ is of full row rank
 8.5 The smooth and impulsive solution components and impulsive free initial conditions: C∞ is not of full row rank
 8.6 Illustrative example
 8.7 Conclusions
 9: A refined resolvent decomposition of a regular polynomial matrix and application to the solution of regular PMDs
 10: Frequency structures of generalized companion form and application to the solution of regular PMDs
 11: A generalized chainscattering representation and its algebraic system properties
 12: Realization of behavior

13: Related extensions to system wellposedness and internal stability
 Abstract
 13.1 Introduction
 13.2 Input consistency, output uniqueness, fully internal wellposedness, and externally internal wellposedness
 13.3 Further characterizations of externally internal wellposedness
 13.4 Generalized linear fractional transformations, externally internal stability, and their characterizations
 13.5 Conclusions
 14: Nonstandard H∞ control problem: A generalized chainscattering representation approach

15: Internet congestion control: A linear multivariable control look
 Abstract
 15.1 The basic model of Internet congestion control
 15.2 Internet congestion control: A multivariable control look
 15.3 Padé approximations to the system (15.7) and (15.8)
 15.4 Analyses into system structure of congestion control of a simple network in frequency domain
 15.5 Conclusions and further discussions
 16: Conclusions and further research
 Bibliography
 Index
Product information
 Title: A Generalized Framework of Linear Multivariable Control
 Author(s):
 Release date: February 2017
 Publisher(s): ButterworthHeinemann
 ISBN: 9780081019474
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