Complex conjugate matrix equations for systems and control
by Wu, Ai-Guo
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 of complex system with structure constraints. It proposes useful approaches to obtain iterative solutions or explicit solutions for several types of complex conjugate matrix equation. It observes th…
Read More ↓Title Statements
- Full title :Complex conjugate matrix equations for systems and control / Ai-Guo Wu, Ying Zhang.
Summary
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 of complex system with structure constraints. It proposes useful approaches to obtain iterative solutions or explicit solutions for several types of complex conjugate matrix equation. It observes that there are some significant differences between the real/complex matrix equations and the complex conjugate matrix equations. For example, the solvability of a real Sylvester matrix equation can be characterized by matrix similarity; however, the solvability of the con-Sylvester matrix equation in complex conjugate form is related to the concept of con-similarity. In addition, the new concept of conjugate product for complex polynomial matrices is also proposed in order to establish a unified approach for solving a type of complex matrix equation.
Read More ↓Edition Statements
- Publication Date:©2017
Publication Statements
- Publisher(s):Springer
- Place of Publication:Singapore
- Language:eng
- Publication Date:©2017
The Physical Object
- Description:1 online resource (xviii, 487 pages) : : illustrations
Edition Identifiers
- ISBN:9789811006371, 9811006377
- oclc:ocn956505378
- LC Classification:QA188
- Dewey Decimal:510
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 …
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