"Generalized Sylvester equations (GSEs) have found applications in many fields, including applied mathematics, systems and control, and signal processing. This book presents a unified parametric approach for solving the various types of GSEs, with proofs theorems and some technical results used. It provides a unified parametric solution formula, in an extremely neat and elegant matrix form, for all the various types of GSEs"-- Read more... Abstract: "Generalized Sylvester equations (GSEs) have found applications in many fields, including applied mathematics, systems and control, and signal processing. This book presents a unified parametric approach for solving the various types of GSEs, with proofs theorems and some technical results used. It provides a unified parametric solution formula, in an extremely neat and elegant matrix form, for all the various types of GSEs" Content: Introduction Three Types of Linear Models Examples of Practical Systems The Sylvester Family An Overview: Work by Other Researchers About the Book Application Highlights of GSEs ESA and Observer Designs Model Reference Tracking and Disturbance Decoupling Sylvester Parametric Control Approaches F-Coprimeness Controllability and Regularizability Coprimeness Equivalent Conditions Regularizable Case Examples Numerical Solution Based on SVD Homogeneous GSEs Sylvester Mappings First-Order GSEs Second-Order GSEs High-Order GSEs Case of F Being in Jordan Form Case of F Being Diagonal Examples Nonhomogeneous GSEs Solution Based on RCF and DPE Condition (5.11) Solution Based on SFR Controllable Case Case of F Being in Jordan Form Case of F Being Diagonal Case of F Being Diagonally Known Examples Fully Actuated GSEs Fully Actuated GSEs Homogeneous GSEs: Forward Solutions Homogeneous GSEs: Backward Solutions Nonhomogeneous GSEs: Forward Solutions Nonhomogeneous GSEs: Backward Solutions Examples GSEs with Varying Coefficients Systems with Varying Coefficients GSEs with Varying Coefficients Fully Actuated GSEs with Varying Coefficients Fully Actuated Homogeneous GSEs Fully Actuated Nonhomogeneous GSEs Examples Rectangular NSEs Rectangular NSEs versus GSEs Case of F Being Arbitrary Case of F Being in Jordan Form Case of F Being Diagonal Case of rank A(s) = n, s C Case of F Being Diagonally Known Square NSEs Case of F Being Arbitrary Case of F Being in Jordan Form Case of F Being Diagonal Example: Constrained Mechanical System NSEs with Varying Coefficients Appendix: Proofs of Theorems References Index Notes and References appear at the end of each chapter. "Generalized Sylvester equations (GSEs) have found applications in many fields, including applied mathematics, systems and control, and signal processing. This book presents a unified parametric approach for solving the various types of GSEs, with proofs theorems and some technical results used. It provides a unified parametric solution formula, in an extremely neat and elegant matrix form, for all the various types of GSEs"-- Provided by publisher Provides One Unified Formula That Gives Solutions to Several Types of GSEsGeneralized Sylvester equations (GSEs) are applied in many fields, including applied mathematics, systems and control, and signal processing. Generalized Sylvester Equations: Unified Parametric Solutions presents a unified parametric approach for solving various types of GSEs
