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 Author Tan, Liansheng, author.

# Title A generalized framework of linear multivariable control / Liansheng Tan.

 Publication Info. Kidlington, Oxford, United Kingdom : Butterworth-Heinemann is an imprint of Elsevier, 2017. ©2017

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 Description 1 online resource text txt rdacontent computer c rdamedia online resource cr rdacarrier Contents Front Cover; A Generalized Framework of Linear Multivariable Control; Copyright; Contents; Chapter 1: Introduction; Chapter 2: Mathematical preliminaries; 2.1 Vector algebra; 2.2 Matrix algebra; 2.2.1 Matrix properties; 2.2.2 Basic matrix operations; 2.3 Matrix inverse; 2.4 Solving system of linear equation; 2.4.1 Gauss method; 2.4.2 A general scheme for solving system of linear equation; 2.5 Linear differential equation; 2.5.1 Introduction; 2.5.2 Homogeneous equations with constant coefficients; 2.5.3 Nonhomogeneous equation with constant coefficients. 2.5.4 Equation with variable coefficients2.5.5 Systems of linear differential equations; 2.6 Matrix differential equation; 2.6.1 Introduction; 2.6.2 Stability and steady state of the matrix system; 2.6.3 Solution in matrix form; 2.6.4 Solving matrix ordinary differential equations; 2.7 Laplace transform; 2.7.1 Introduction; 2.7.2 Formal definition; 2.7.3 Region of convergence; 2.7.4 Laplace transform pair table; 2.7.5 Properties and theorems; 2.7.6 Inverse Laplace transform; Chapter 3: Generalized inverse of matrix and solution of linear system equation; 3.1 The generalized inverse of matrix. 3.1.1 The left inverse and right inverse3.1.2 Moore-Penrose inverse; 3.1.3 The minimization approach to solve an algebraic matrix equation; 3.2 The full rank decomposition theorem; 3.3 The least square solution to an algebraic matrix equation; 3.3.1 The solution to the compatible linear equations; 3.3.2 The least square solution of incompatible equation; 3.3.3 The minimum norm least squares solution for the equations; 3.4 The singular value decomposition; Chapter 4: Polynomial fraction description; 4.1 Introduction; 4.2 Right polynomial fractions; 4.3 Left polynomial fraction. 4.4 Column and row degrees4.5 Minimal realization; 4.6 Poles and zeros; 4.7 State feedback; Chapter 5: Stability; 5.1 Internal stability; 5.1.1 Uniform exponential stability; 5.1.2 Uniform asymptotic stability; 5.1.3 Lyapunov transformation; 5.2 Lyapunov stability; 5.2.1 Introduction; 5.2.2 Uniform stability; 5.2.3 Uniform exponential stability; 5.2.4 Instability; 5.2.5 Time-invariant case; 5.3 Input-output stability; 5.3.1 Uniform bounded-input bounded-output stability; 5.3.2 Relation to uniform exponential stability; 5.3.3 Time-invariant case. Chapter 6: Fundamental approaches to control system analysis6.1 PMD theory of linear multivariable control systems; 6.2 Behavioral approach in systems theory; 6.3 Chain-scattering representations; 6.4 Conclusions; Chapter 7: Determination of finite and infinite frequency structure of a rational matrix; 7.1 Introduction; 7.2 The Toeplitz rank information; 7.3 To determine the Smith form of a polynomial matrix; 7.4 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. Bibliography Includes bibliographical references and index. Note Online resource; title from PDF title page (ScienceDirect, viewed February 17, 2017). Summary 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. Subject H infinity symbol control. TECHNOLOGY & ENGINEERING -- Engineering (General) H [infinity symbol] control. (OCoLC)fst00949812 Other Form: Print version: Tan, Liansheng. Generalized framework of linear multivariable control. ©2017 0081019467 9780081019467 (OCoLC)960901240 ISBN 9780081019474 (electronic bk.) 0081019475 (electronic bk.) 9780081019467 (print) 0081019467 Standard No. AU@ 000059703170 AU@ 000066135177 CHBIS 011069596 CHNEW 001014126 CHVBK 499790111 GBVCP 881720127 GBVCP 897159152 UKMGB 018189274

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