Complex conjugate matrix equations for systems and control / Ai-Guo Wu, Ying Zhang.

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