In this book the authors reduce a wide variety of problems arising in system and control theory to a handful of convex and quasiconvex optimization problems that involve linear matrix inequalities. These optimization problems can be solved using recently developed numerical algorithms that not only are polynomial-time but also work very well in practice; the reduction therefore can be considered a solution to the original problems. This book opens up an important new research area in which convex optimization is combined with system and control theory, resulting in the solution of a large number of previously unsolved problems.
Special Features - The book identifies a handful of standard optimization problems that are general (a wide variety of problems from system and control theory can be reduced to them) as well as specific (specialized numerical algorithms can be devised for them).
- The book catalogs a diverse list of problems in system and control theory that can be reduced to the standard optimization problems. Problems considered are analysis and state-feedback design for uncertain systems, matrix analysis problems, and many others.
- Most of the the book is accessible to anyone with a basic mathematics background, e.g., linear algebra and differential equations.
Partial Contents Preface; Chapter 1: Introduction; Chapter 2: Some Standard Problems Involving LMIs; Chapter 3: Some Matrix Problems; Chapter 4: Linear Differential Inclusions; Chapter 5: Analysis of LDIs: State Properties; Chapter 6: Analysis of LDIs: Input/Output Properties; Chapter 7: State-Feedback Synthesis for LDIs; Chapter 8: Lur'e and Multiplier Methods; Chapter 9: Systems with Multiplicative Noise; Chapter 10: Miscellaneous Problems; Notation; List of Acronyms; Bibliography; Index.
Audience This book is primarily intended for researchers in system and control theory; both the beginner and the advanced researcher will find the book useful. Researchers in convex optimization will find this book a source of optimization problems for which algorithms need to be devised. A background in linear algebra, elementary analysis, and exposure to differential equations and system and control theory is recommended.