图书信息:

书  名:Generalized Sylvester Equations Unified Parametric Solutions
作  者:Guang-Ren Duan
出 版 社:CRC Press
出版日期:2015年3月
语  种:英 文
I S B N:978-1-4822-4396-3
页  数:451

内容简介:   

  本书建立了多种形式的广义Sylvester矩阵方程的参数化解。全书共有九个章节和一个附录。第一章介绍了本书中讨论的广义Sylvester方程(GSEs)的各种形式,并对GSEs的解给出了一个简要的概述。第二章用四个典型的控制设计应用说明了GSEs的重要性。第三章介绍和讨论了多项式矩阵对的F-互质性,这一概念在本书中起到了基础作用。第四章到第七章讨论了GSEs的解。特别地,第四章和第五章分别展示了广义齐次和非齐次GSEs的解。在第六章中,通过简化前两章的解,给出了一类特殊形式GSEs,即全驱GSEs的一般解,并在第七章中,将结果进一步推广到带有变系数的GSEs中。第八章提出了一个广义高阶矩形标准Sylvester方程(NSEs),并且表明了这些矩形NSEs仅仅是GSEs的不同表现形式,因此这些方程的参数解可以自然地基于齐次和非齐次GSEs的解得到。第九章通过简化全驱GSEs的解,得到了方形NSEs的解,包括著名的连续和离散Lyapunov方程的解。附录中包含了第三章和第五章中一些定理的证明。

  本书可以作为应用数学和控制系统理论与应用专业的高年级本科生或者研究生的课程的主要或者次要的教材,也可以作为机械工程、电力工程和航空航天工程专业的教材;也可以作为控制系统与应用、应用数学、机械工程、电力工程和航空航天工程专业的研究生、研究员、科学家、工程师和大学教师的参考书。

图书目录:

Preface
Notations
Abbreviations
1  Introduction
  1.1  Three Types of Linear Models
    1.1.1  First-Order Systems
    1.1.2  Second-Order Systems
    1.1.3  Higher-Order Systems
  1.2  Examples of Practical Systems
    1.2.1  Circuit System
    1.2.2  Multiagent Kinematic Systems
    1.2.3  Constrained Linear Mechanical Systems
      1.2.3.1  Matrix Second-Order Form
      1.2.3.2  Matrix First-Order Form
    1.2.4  Flexible-Joint Robots
  1.3  Sylvester Family
    1.3.1  First-Order GSEs
      1.3.1.1  Homogeneous GSEs
      1.3.1.2  Nonhomogeneous GSEs
    1.3.2  Second-Order GSEs
    1.3.3  Higher-Order GSEs
    1.3.4  NSEs
  1.4  An Overview:Work by Other Researchers
    1.4.1  GSEs Related to Normal Linear Systems
      1.4.1.1  Numerical Solutions
      1.4.1.2  Parametric Solutions
      1.4.1.3  Solutions with Applications
    1.4.2  GSEs Related to Descriptor Linear Systems
      1.4.2.1  Solutions to the Equations
      1.4.2.2  Solutions with Applications
    1.4.3  Other Types of Equations
      1.4.3.1  Nonhomogeneous First-Order GSEs
      1.4.3.2  Second- and Higher-Order GSEs
  1.5  About the Book
    1.5.1  Purposes
      1.5.1.1  Showing Applications of GSEs
      1.5.1.2  Highlighting the Sylvester Parametric Approaches
      1.5.1.3  Presenting Solutions to GSEs.
    1.5.2  Structure
    1.5.3  Basic Formulas
      1.5.3.1  Formula Set I for the Case of Arbitrary F
      1.5.3.2  Formula Set II for the Case of Jordan Matrix F
      1.5.3.3  Formula Set III for the Case of Diagonal F
    1.5.4  Features
      1.5.4.1  General Suitability
      1.5.4.2  High Unification
      1.5.4.3  Completeness in Degrees of Freedom
      1.5.4.4  Neatness and Simplicity
      1.5.4.5  Numerical Simplicity and Reliability
2  Application Highlights of GSEs
  2.1  ESA and Observer Designs
    2.1.1  Generalized Pole/ESA
      2.1.1.1  State Feedback Case
      2.1.1.2  Output Feedback Case
      2.1.1.3  Comments and Remarks
    2.1.2  Observer Design
      2.1.2.1  Luenberger Observers
      2.1.2.2  PI Observers
      2.1.2.3  Comments and Remarks
  2.2  Model Reference Tracking and Disturbance Decoupling
    2.2.1  Model Reference Tracking
    2.2.2  Disturbance Rejection
  2.3  Sylvester Parametric Control Approaches
    2.3.1  General Procedure
    2.3.2  Main Steps
      2.3.2.1  Solving GSEs
      2.3.2.2  Controller Parametrization
      2.3.2.3  Specification Parametrization
      2.3.2.4  Parameter Optimization
  2.4  Notes and References
    2.4.1  Problem of ESA in Higher-Order Systems
    2.4.2  Author's Work on Sylvester Parametric Approaches
      2.4.2.1  ESA
      2.4.2.2  Observer Design
      2.4.2.3  Fault Detection
      2.4.2.4  Disturbance Decoupling
      2.4.2.5  Robust Pole Assignment
3  F-Coprimeness
  3.1  Controllability and Regularizability
    3.1.1  First-Order Systems
     3.1.1.1  Controllability and Stabilizability
     3.1.1.2  Regularity and Regularizability
    3.1.2  Higher-Order Systems
      3.1.2.1  Controllability and Stabilizability
      3.1.2.2  Regularity and Regularizability
  3.2  Coprimeness
    3.2.1  Existing Concepts
    3.2.2  Generalized Concepts
    3.2.3  Coprimeness of A(s) and B(s)
      3.2.3.1  Irregularizable Case
      3.2.3.2  Regularizable Case
  3.3  Equivalent Conditions
    3.3.1  SFR
    3.3.2  Generalized RCF
    3.3.3  DPE
    3.3.4  Unified Procedure
  3.4  Regularizable Case
    3.4.1  F-Left Coprime with Rank n
      3.4.1.1  Equivalent Conditions
      3.4.1.2  Unified Procedure
    3.4.2  Controllability
      3.4.2.1  Equivalent Conditions
      3.4.2.2  Unified Procedure
  3.5  Examples
    3.5.1  First-Order Systems
    3.5.2  Second-Order Systems
    3.5.3  Higher-Order Systems
  3.6  Numerical Solution Based on SVD
    3.6.1  Problem Description
    3.6.2  Main Steps
      3.6.2.1  Data Generation via SVD
      3.6.2.2  Polynomial Recovering
    3.6.3  Numerical Solution
  3.7  Notes and References
    3.7.1  Coprime Factorizations
    3.7.2  Unified Procedure
    3.7.3  Numerical Algorithm Using SVD
4  Homogeneous GSEs
  4.1  Sylvester Mappings
    4.1.1  Definition and Operations
    4.1.2  Representation of GSEs
  4.2  First-Order GSEs
    4.2.1  General Solution
    4.2.2  Example
  4.3  Second-Order GSEs
    4.3.1  General Solution
    4.3.2  Example
  4.4  Higher-Order GSEs
    4.4.1  General Solution
    4.4.2  Example
  4.5  Case of F Being in Jordan Form
    4.5.1  General Solution
    4.5.2  Example
  4.6  Case of F Being Diagonal
    4.6.1  Case of Undetermined F
    4.6.2  Case of Determined F
  4.7  Examples
    4.7.1  First-Order Systems
    4.7.2  Second-Order Systems
    4.7.3  Higher-Order Systems
  4.8  Notes and References
    4.8.1  GSEs Associated with Normal Linear Systems
    4.8.2  GSEs Associated with Descriptor Linear Systems
    4.8.3  Second-Order GSEs
    4.8.4  Higher-Order GSEs
    4.8.5  Other Related Results
      4.8.5.1  Numerical Solutions of GSEs
      4.8.5.2  Sylvester-Conjugate Matrix Equations
5  Nonhomogeneous GSEs
  5.1  Solution Based on RCF and DPE
    5.1.1  Particular Solution
    5.1.2  General Solution
    5.1.3  Solution to GSE (1.70)
  5.2  Condition (5.11)
    5.2.1  Solution of R’
    5.2.2  Regularizable Case
  5.3  Solution Based on SFR
    5.3.1  Particular Solution
    5.3.2  General Solution
  5.4  Controllable Case
    5.4.1  Results
    5.4.2  Examples
  5.5  Case of F Being in Jordan Form
    5.5.1  Solution Based on RCF and DPE
    5.5.2  Solution Based on SFR
    5.5.3  Example
  5.6  Case of F Being Diagonal
    5.6.1  Solution Based on RCF and DPE
    5.6.2  Solution Based on SFR
    5.6.3  Example
  5.7  Case of F Being Diagonally Known
    5.7.1  SFR and SVD
      5.7.1.1  Discretized RCF and DPE
      5.7.1.2  Discretized Form of Condition (5.11)
    5.7.2  Solution Based on SVD
  5.8  Examples
    5.8.1  First-Order Systems
    5.8.2  Second-Order Systems
    5.8.3  Higher-Order Systems
  5.9  Notes and References
    5.9.1  First-Order GSEs
    5.9.2  Second- and Higher-Order GSEs
6  Fully Actuated GSEs
  6.1  Fully Actuated GSEs
    6.1.1  Fully Actuated Systems
    6.1.2  Fully Actuated GSEs
    6.1.3  Examples
  6.2  Homogeneous GSEs: Forward Solutions
    6.2.1  General Solutions
      6.2.1.1  Case of F Being Arbitrary
      6.2.1.2  Case of F Being in Jordan Form
      6.2.1.3  Case of F Being Diagonal
      6.2.1.4  Standard Fully Actuated GSEs
    6.2.2  Type of Second-Order GSEs
  6.3  Homogeneous GSEs: Backward Solutions
    6.3.1  General Solutions
      6.3.1.1  Case of F Being Arbitrary
      6.3.1.2  Case of F Being a Jordan Matrix
      6.3.1.3  Case of F Being Diagonal
    6.3.2  Standard Fully Actuated GSEs
  6.4  Nonhomogeneous GSEs: Forward Solutions
    6.4.1  Case of F Being Arbitrary
    6.4.2  Case of F Being in Jordan Form
    6.4.3  Case of F Being Diagonal
    6.4.4  Type of Second-Order GSEs
  6.5  Nonhomogeneous GSEs: Backward Solutions
    6.5.1  Case of F Being Arbitrary
    6.5.2  Case of F Being in Jordan Form
    6.5.3  Case of F Being Diagonal
  6.6  Examples
  6.7  Notes and References
    6.7.1  Utilizing the Advantage
    6.7.2  ESA in Fully Actuated Systems
    6.7.3  Space Rendezvous Control
7  GSEs with Varying Coefficients
  7.1  Systems with Varying Coefficients
    7.1.1  Examples of First-Order Systems
      7.1.1.1  Nonlinear Systems
      7.1.1.2  Quasilinear Systems
    7.1.2  Examples of Second-Order Systems
      7.1.2.1  Time-Varying Linear Systemsn
      7.1.2.2  Quasilinear Systems
  7.2  GSEs with Varying Coefficients
    7.2.1  F-Left Coprimeness
    7.2.2  Solutions
      7.2.2.1  Homogeneous GSEs
      7.2.2.2  Nonhomogeneous GSEs
    7.2.3  Example
  7.3  Fully Actuated GSEs with Varying Coefficients
    7.3.1  Definitions
    7.3.2  Examples
  7.4  Fully Actuated Homogeneous GSEs
    7.4.1  Forward Solutions
      7.4.1.1  Case of F Being Arbitrary
      7.4.1.2  Case of F Being in Jordan Form
      7.4.1.3  Case of F Being Diagonal
    7.4.2  Backward Solutions
      7.4.2.1  Case of F Being Arbitrary
      7.4.2.2  Case of F Being in Jordan Form
      7.4.2.3  Case of F Being Diagonal
  7.5  Fully Actuated Nonhomogeneous GSEs
    7.5.1  Forward Solutions
      7.5.1.1  Case of F Being Arbitrary
      7.5.1.2  Case of F Being in Jordan Form
      7.5.1.3  Case of F Being Diagonal
    7.5.2  Backward Solutions
      7.5.2.1  Case of F Being Arbitrary
      7.5.2.2  Case of F Being in Jordan Form
      7.5.2.3  Case of F Being Diagonal
  7.6  Examples
    7.6.1  Space Rendezvous Systems
    7.6.2  Robotic Systems
  7.7  Notes and References
    7.7.1  Further Comments
    7.7.2  Space Rendezvous Control: The General Case
      7.7.2.1  Problem
      7.7.2.2  Direct Parametric Approach
      7.7.2.3  Example
8  Rectangular NSEs
  8.1  Rectangular NSEs versus GSEs
    8.1.1  Rectangular NSEs
    8.1.2  Deriving NSEs by Specifying GSEs
    8.1.3  Converting GSEs into NSEs
    8.1.4  Assumption
  8.2  Case of F Being Arbitrary
    8.2.1  SFR of A(s)
    8.2.2  Homogeneous NSEs
    8.2.3  Nonhomogeneous NSEs
      8.2.3.1  Particular Solution
      8.2.3.2  General Solution
  8.3  Case of F Being in Jordan Form
    8.3.1  Homogeneous NSEs
    8.3.2  Nonhomogeneous NSEs
  8.4  Case of F Being Diagonal
    8.4.1  Homogeneous NSEs
    8.4.2  Nonhomogeneous NSEs
    8.4.3  Example
  8.5  Case of rank A(s) = n, ∀s ∈ C
    8.5.1  Homogeneous NSEs
    8.5.2  Nonhomogeneous NSEs
    8.5.3  Example
  8.6  Case of F Being Diagonally Known
    8.6.1  SFR and SVD
    8.6.2  Solutions
    8.6.3  Example
  8.7  Notes and References
    8.7.1  Comments
    8.7.2  Combined GSEs
9  Square NSEs
  9.1  Case of F Being Arbitrary
    9.1.1  Solution
    9.1.2  Special Cases
      9.1.2.1  First-Order NSEs
      9.1.2.2  Lyapunov Equations
  9.2  Case of F Being in Jordan Form
    9.2.1  General Solution
    9.2.2  Special Cases
      9.2.2.1  First-Order NSEs
      9.2.2.2  Lyapunov Equations
  9.3  Case of F Being Diagonal
    9.3.1  General Solution
    9.3.2  First-Order NSEs and Lyapunov Equations
      9.3.2.1  First-Order NSEs
      9.3.2.2  Lyapunov Equations
  9.4  Example: Constrained Mechanical System results
  9.5  NSEs with Varying Coefficients
    9.5.1  Case of F Being Arbitrary
    9.5.2  Case of F Being in Jordan Form
    9.5.3  Case of F Being Diagonal
  9.6  Notes and References
    9.6.1  Comments on Results
    9.6.2  Existing Solutions
      9.6.2.1  NSEs
      9.6.2.2  Lyapunov Matrix Equations
Appendix A : Proofs of Theorems
  A.1 Proof of Theorem 3.6
    A.1.1 Preliminary Lemma
    A.1.2 Proof of Theorem 3.6
  A.2 Proof of Theorem 3.13
    A.2.1 Preliminary Lemmas
    A.2.2 Proof of Theorem 3.13
  A.3 Proof of Theorem 4.1
    A.3.1 Proof of Conclusion 1
    A.3.2 Proof of Conclusion 2
    A.3.3 Proof of Conclusion 3
    A.3.4 Proof of Conclusion 4
  A.4 Proofs of Theorems 4.2, 4.4, and 4.6
  A.5 Proofs of Theorems 4.3, 4.5, and 4.7
References
Index


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