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قیمت: 2000 تومان

Generalized Sylvester Equations: Unified Parametric Solutions

By


شناسنامه فارسی کتاب:
عنوان کتاب:

تعمیم سیلوستر معادلات: راه حل های یکپارچه پارامتری

موضوع کتاب:

Technique, Electronics, Signal Processing

سال نشر:
ناشر: CRC Press
ویرایش:
شماره جلد:
تعداد صفحه: C, xxiv, 430, B
زبان: انگلیسی
Features
Covers several types of very general GSEs, including GSEs with arbitrary orders, arbitrary dimensions, unknown parameter matrices, and GSEs without controllability or regularizability assumption
Proposes a whole set of highly unified parametric general solutions to the various types of GSEs, which are in very simple and neat analytical closed-forms and are complete in the sense of providing all the degrees of freedom
Presents numerically simple and reliable unified procedures using matrix elementary transformations or singular value decompositions for solving the relevant polynomial matrices based on which general solutions to the GSEs can be immediately constructed

Provides One Unified Formula That Gives Solutions to Several Types of GSEs

Generalized 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.

In an extremely neat and elegant matrix form, the book provides a single unified parametric solution formula for all the types of GSEs, which further reduces to a specific clear vector form when the parameter matrix F in the equations is a Jordan matrix. Particularly, when the parameter matrix F is diagonal, the reduced vector form becomes extremely simple.

The first chapter introduces several types of GSEs and gives a brief overview of solutions to GSEs. The two subsequent chapters then show the importance of GSEs using four typical control design applications and discuss the F-coprimeness of a pair of polynomial matrices. The next several chapters deal with parametric solutions to GSEs. The final two chapters present analytical solutions to normal Sylvester equations (NSEs), including the well-known continuous- and discrete-time Lyapunov equations. An appendix provides the proofs of some theorems.

The book can be used as a reference for graduate and senior undergraduate courses in applied mathematics and control systems analysis and design. It will also be useful to readers interested in research and applications based on Sylvester equations.
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.
شابک/ISBN: 1482243962, 9781482243963