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 H-infinity control, the linear fractional transformation formulation is relying on the inverse of the block matrix. If the block matrix is not regular, the H-infinity 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 non-regular 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 chain-scattering representation and its algebraic system properties
- 12: Realization of behavior
-
13: Related extensions to system well-posedness and internal stability
- Abstract
- 13.1 Introduction
- 13.2 Input consistency, output uniqueness, fully internal well-posedness, and externally internal well-posedness
- 13.3 Further characterizations of externally internal well-posedness
- 13.4 Generalized linear fractional transformations, externally internal stability, and their characterizations
- 13.5 Conclusions
- 14: Nonstandard H∞ control problem: A generalized chain-scattering 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): Butterworth-Heinemann
- ISBN: 9780081019474
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