Elsevier S & T

Lyapunov Matrix Equation in System Stability and Control: Mathematics in Science and Engineering V195

Gajic, Zoran; Qureshi, Muhammad Tahir Javed

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Table of contents
  • Cover
  • Contentsvii
  • Prefacexi
  • Chapter 1. Introduction1
  • 1.1 Stability of Linear Systems5
  • 1.2 Variance of Linear Stochastic Systems8
  • 1.3 Quadratic Performance Measure9
  • 1.4 Book Organization11
  • 1.5 References15
  • Chapter 2. Continuous Algebraic Lyapunov Equation21
  • 2.1 Explicit Solutions22
  • 2.2 Solution Bounds39
  • 2.3 Numerical Solutions62
  • 2.4 Summary70
  • 2.5 References71
  • Chapter 3. Discrete Algebraic Lyapunov Equation79
  • 3.1 Explicit Solutions80
  • 3.2 Bounds of Solution's Attributes85
  • 3.3 Numerical Solutions99
  • 3.4 Summary101
  • 3.5 References102
  • Chapter 4. Differential and Difference Lyapunov Equations107
  • 4.1 Explicit Solutions108
  • 4.2 Bounds of Solution's Attributes111
  • 4.3 Numerical Solutions116
  • 4.4 Singularly Perturbed and Weakly Coupled Systenns120
  • 4.5 Coupled Differential Lyapunov Equations128
  • 4.6 Sunnmary130
  • 4.7 References130
  • Chapter 5. Algebraic Lyapunov Equations with Small Parameters133
  • 5.1 Singularly Perturbed Continuous Lyapunov Equation136
  • 5.2 Weakly Coupled Continuous Lyapunov Equation141
  • 5.3 Singularly Perturbed Discrete Systems143
  • 5.4 Recursive Methods for Weakly Coupled Discrete Systems148
  • 5.5 Summary150
  • 5.6 References151
  • Chapter 6. Stability Robustness and Sensitivity of Lyapunov Equation155
  • 6.1 Stability Robustness155
  • 6.2 Sensitivity162
  • 6.3 References166
  • Chapter 7. Iterative Methods and Parallel Algorithms169
  • 7.1 Smith's Algorithm170
  • 7.2 ADI Iterative Method172
  • 7.3 SOR Iterative Method174
  • 7.4 Parallel Algorithms175
  • 7.5 Parallel Algorithms for Coupled Lyapunov Equations178
  • 7.6 Comments184
  • 7.7 References185
  • Chapter 8. Lyapunov Iterations189
  • 8.1 Kleinman's Algorithm for Riccati Equation190
  • 8.2 Lyapunov Iterations for Jump Parameter Linear Systems195
  • 8.3 Lyapunov Iterations for Nash Differential Games208
  • 8.4 Lyapunov Iterations for Output Feedback Control215
  • 8.5 Comments218
  • 8.6 References218
  • Chapter 9. Concluding Remarks223
  • 9.1 Sylvester Equations223
  • 9.2 Related Topics227
  • 9.3 Applications228
  • 9.4 Comments233
  • 9.5 References234
  • Appendix243
  • Matrix Inequalities243
  • Index251
Book details
  • Vendor Elsevier S & T
  • SKU 9780122733703
  • ISBN-13 9780080535678
  • Author Gajic, Zoran; Qureshi, Muhammad Tahir Javed
  • Category Mathematics
  • Subject Applied

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Description eBook delivery & access Reviews
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.
The Lyapunov Matrix Equation in System Stability and Control 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.
The book will appeal to practicing engineers, theoreticians, applied mathematicians, and graduate students who seek a comprehensive view of the main results of the Lyapunov matrix equation.

Presents techniques for solving and analyzing the algebraic, differential, and difference Lyapunov matrix equations of continuous-time and discrete-time systems
Offers summaries and references at the end of each chapter
Contains examples of the use of the equation to solve real-world problems
Provides quick and easy references for the solutions to engineering and mathematical problems using the Lyapunov equation