book

A Generalized Framework of Linear Multivariable Control

Name: A Generalized Framework of Linear Multivariable Control
Author: Liansheng Tan
ISBN: 9780081019474

by Liansheng Tan

February 2017

Intermediate to advanced

322 pages

10h 49m

English

Butterworth-Heinemann

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Cover image
Title page
Table of Contents
Copyright
1: Introduction
Abstract
2: Mathematical preliminaries
Abstract2.1 Vector algebra2.2 Matrix algebra2.3 Matrix inverse2.4 Solving system of linear equation2.5 Linear differential equation2.6 Matrix differential equation2.7 Laplace transform
3: Generalized inverse of matrix and solution of linear system equation
Abstract3.1 The generalized inverse of matrix3.2 The full rank decomposition theorem3.3 The least square solution to an algebraic matrix equation3.4 The singular value decomposition
4: Polynomial fraction description
Abstract4.1 Introduction4.2 Right polynomial fractions4.3 Left polynomial fraction4.4 Column and row degrees4.5 Minimal realization
4.6 Poles and zeros
4.7 State feedback
5: Stability
Abstract5.1 Internal stability5.2 Lyapunov stability5.3 Input-output stability

6: Fundamental approaches to control system analysis
Abstract6.1 PMD theory of linear multivariable control systems6.2 Behavioral approach in systems theory6.3 Chain-scattering representations6.4 Conclusions
7: Determination of finite and infinite frequency structure of a rational matrix
Abstract7.1 Introduction7.2 The Toeplitz rank information7.3 To determine the Smith form of a polynomial matrix7.4 To determine the Smith-McMillan form at infinity of a rational matrix
7.5 To determine the Smith-McMillan form of a rational matrix
7.6 Conclusions
8: The solution of a regular PMD and the set of impulsive free initial conditions
Abstract8.1 Introduction8.2 Preliminary results8.3 A solution for the LNHMDEs8.4 The smooth and impulsive solution components and impulsive free initial conditions: C∞ is of full row rank8.5 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
Abstract9.1 Introduction9.2 Infinite Jordan pairs9.3 The solution of regular PMDs9.4 Algorithm and examples
9.5 Conclusions
10: Frequency structures of generalized companion form and application to the solution of regular PMDs
Abstract10.1 Introduction10.2 The frequency structures of generalized companion form and a new resolvent decomposition10.3 Application to the solution of regular PMDs10.4 Conclusions
11: A generalized chain-scattering representation and its algebraic system properties
Abstract11.1 Introduction11.2 Input-output consistency and GCSR11.3 Algebraic system properties of GCSR and DGCSR11.4 Realizations of GCSR and DGCSR11.5 Conclusions
12: Realization of behavior
Abstract12.1 Introduction12.2 Behavior realization12.3 Realization of behavior for GCSRs and DGCSRs12.4 Conclusions
13: Related extensions to system well-posedness and internal stability
Abstract13.1 Introduction13.2 Input consistency, output uniqueness, fully internal well-posedness, and externally internal well-posedness13.3 Further characterizations of externally internal well-posedness13.4 Generalized linear fractional transformations, externally internal stability, and their characterizations13.5 Conclusions
14: Nonstandard H∞ control problem: A generalized chain-scattering representation approach
Abstract14.1 Introduction14.2 Reformulation of the nonstandard H∞ control problem via generalized chain-scattering representation14.3 Solvability of nonstandard H∞ control problem14.4 Conclusions
15: Internet congestion control: A linear multivariable control look
Abstract15.1 The basic model of Internet congestion control15.2 Internet congestion control: A multivariable control look15.3 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
Abstract
Bibliography
Index

Content preview from A Generalized Framework of Linear Multivariable Control

$\begin{array}{l} \begin{matrix} J_{\infty}^{'} & = [0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] \\ [0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] \\ [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] \\ [0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] \\ [0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] \\ [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] \\ [0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] \\ [0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] \\ [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] \\ [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] \\ [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] \\ [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] \\ [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0] \\ [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0] \\ [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0] \\ [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0] \\ [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] \end{matrix} \end{array}$

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A Generalized Framework of Linear Multivariable Control

by Liansheng Tan

Become an O’Reilly member and get unlimited access to this title plus top books and audiobooks from O’Reilly and nearly 200 top publishers, thousands of courses curated by job role, 150+ live events each month,
and much more.