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.
General
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