The Lyapunov Matrix Equation in System Stability and Control
Published on 1. January 1995
Book
Hardback
240 pages
978-0-12-273370-3 (ISBN)
Description
The Lyapunov and Riccati equations are two of the fundamental equations of control and system theory, having special relevance for system identification, optimization, boundary value problems, power systems, signal processing, and communications. This study covers mathematical developments and applications while providing quick and easy references for solutions to engineering and mathematical problems. Examples of real-world systems are given throughout the text in order to demonstrate the effectiveness of the presented methods and algorithms. It should appeal to practicing engineers, theoreticians, applied mathematicians, and graduate students who seek a comprehensive view of the main results of the Lyapunov matrix equation. The text includes: techniques for solving and analysing the algebraic, differential, and difference Lyapunov matrix equations of continuous-time and discrete-time systems; summaries and references at the end of each chapter; examples of the use of the equation to solve real-world problems; and quick and easy references for the solutions to engineering and mathematical problems using the Lyapunov equation.
More details
Series
Language
English
Place of publication
San Diego
United States
Publishing group
Elsevier Science Publishing Co Inc
Target group
College/higher education
Professional and scholarly
Illustrations
illustrations, indexes
Dimensions
Height: 234 mm
Width: 158 mm
Weight
549 gr
ISBN-13
978-0-12-273370-3 (9780122733703)
Copyright in bibliographic data is held by Nielsen Book Services Limited or its licensors: all rights reserved.
Schweitzer Classification
Other editions
Additional editions
Zoran Gajic | Muhammad Tahir Javed Qureshi
Lyapunov Matrix Equation in System Stability and Control
E-Book
08/1995
Academic Press
€48.95
Available for download
Content
Part 1 Introduction: stability of linear systems; variance of linear stochastic systems; quadratic performance measure; book organization. Part 2 Continuous algebraic Lyapunov equation: explicit solutions; solution sounds; numerical solutions. Part 3 Discrete algebraic Lyapunov equation: explicit solutions; bounds of solution's attributes; numerical solutions. Part 4 Differential and difference Lyapunov equation: explicit solutions; bounds of solution's attributes; numerical solutions; singularly perturbed and weakly coupled systems; coupled differential equations. Part 5 Algebraic Lyapunov equation with small parameters: singularly perturbed continuous Lyapunov equation; weakly coupled continuous Lyapunov equation; singularly perturbed discrete systems; recursive methods for weakly coupled discrete systems. Part 6 Robustness and sensitivity of the Lyapunov equation: stability robustness; sensitivity of algebraic Lyapunov equation. Part 7 Iterative methods and parallel algorithms: Smith's algorithm; ADI iterative method; SOR iterative method; parallel algorithms; parallel algorithms for coupled Lyapunov equations. Part 8 Lyapunov iterations: Kleinman algorithm for Riccati equation; Lyapunov iterations for jump linear systems; Lyapunov iterations for Nash differential games; Lyapunov iterations for output feedback control. Part 9 Concluding remarks: Sylvester equations; related topics; applications. Appendix: matrix inequalities.