Complex conjugate matrix equations for systems and control

• Main Authors: Wu, Ai-Guo (Author), Zhang, Ying (Author)
• Format: Electronic eBook
• Language: English
• Published: Singapore : Springer, 2016.
• Series: Communications and control engineering.
• Subjects: Matrices.; elektronické knihy; electronic books
• ISBN: 9789811006371; 9789811006357
• ISSN: 0178-5354
• Physical Description: 1 online resource (xviii, 487 pages) : illustrations

The book is the first book on complex matrix equations including the conjugate of unknown matrices. The study of these conjugate matrix equations is motivated by the investigations on stabilization and model reference tracking control for discrete-time antilinear systems, which are a particular kind...

Table of Contents:

• Preface; Contents; Notation; 1 Introduction; 1.1 Linear Equations; 1.2 Univariate Linear Matrix Equations; 1.2.1 Lyapunov Matrix Equations; 1.2.2 Kalman-Yakubovich and Normal Sylvester Matrix Equations; 1.2.3 Other Matrix Equations; 1.3 Multivariate Linear Matrix Equations; 1.3.1 Roth Matrix Equations; 1.3.2 First-Order Generalized Sylvester Matrix Equations; 1.3.3 Second-Order Generalized Sylvester Matrix Equations; 1.3.4 High-Order Generalized Sylvester Matrix Equations; 1.3.5 Linear Matrix Equations with More Than Two Unknowns; 1.4 Coupled Linear Matrix Equations.
• 1.5 Complex Conjugate Matrix Equations1.6 Overview of This Monograph; 2 Mathematical Preliminaries; 2.1 Kronecker Products; 2.2 Leverrier Algorithms; 2.3 Generalized Leverrier Algorithms; 2.4 Singular Value Decompositions; 2.5 Vector Norms and Operator Norms; 2.5.1 Vector Norms; 2.5.2 Operator Norms; 2.6 A Real Representation of a Complex Matrix; 2.6.1 Basic Properties; 2.6.2 Proof of Theorem 2.7; 2.7 Consimilarity; 2.8 Real Linear Spaces and Real Linear Mappings; 2.8.1 Real Linear Spaces; 2.8.2 Real Linear Mappings; 2.9 Real Inner Product Spaces; 2.10 Optimization in Complex Domain.
• 2.11 Notes and ReferencesPart I Iterative Solutions; 3 Smith-Type Iterative Approaches; 3.1 Infinite Series Form of the Unique Solution; 3.2 Smith Iterations; 3.3 Smith (l) Iterations; 3.4 Smith Accelerative Iterations; 3.5 An Illustrative Example; 3.6 Notes and References; 4 Hierarchical-Update-Based Iterative Approaches; 4.1 Extended Con-Sylvester Matrix Equations; 4.1.1 The Matrix Equation AXB+CoverlineXD=F; 4.1.2 A General Case; 4.1.3 Numerical Examples; 4.2 Coupled Con-Sylvester Matrix Equations; 4.2.1 Iterative Algorithms; 4.2.2 Convergence Analysis; 4.2.3 A More General Case.
• 4.2.4 A Numerical Example4.3 Complex Conjugate Matrix Equations with Transpose of Unknowns; 4.3.1 Convergence Analysis; 4.3.2 A Numerical Example; 4.4 Notes and References; 5 Finite Iterative Approaches; 5.1 Generalized Con-Sylvester Matrix Equations; 5.1.1 Main Results; 5.1.2 Some Special Cases; 5.1.3 Numerical Examples; 5.2 Extended Con-Sylvester Matrix Equations; 5.2.1 The Matrix Equation AXB+CoverlineXD=F; 5.2.2 A General Case; 5.2.3 Numerical Examples; 5.3 Coupled Con-Sylvester Matrix Equations; 5.3.1 Iterative Algorithms; 5.3.2 Convergence Analysis; 5.3.3 A More General Case.
• 5.3.4 Numerical Examples5.3.5 Proofs of Lemmas 5.15 and 5.16; 5.4 Notes and References; Part II Explicit Solutions; 6 Real-Representation-Based Approaches; 6.1 Normal Con-Sylvester Matrix Equations; 6.1.1 Solvability Conditions; 6.1.2 Uniqueness Conditions; 6.1.3 Solutions; 6.2 Con-Kalman-Yakubovich Matrix Equations; 6.2.1 Solvability Conditions; 6.2.2 Solutions; 6.3 Con-Sylvester Matrix Equations; 6.4 Con-Yakubovich Matrix Equations; 6.5 Extended Con-Sylvester Matrix Equations; 6.6 Generalized Con-Sylvester Matrix Equations; 6.7 Notes and References; 7 Polynomial-Matrix-Based Approaches.