Linear Matrix Inequalities in System and Control Theory

Linear Matrix Inequalities in System and Control Theory is a comprehensive technical text that introduces Linear Matrix Inequalities (LMIs) and their applications in control system analysis and design. The book combines mathematical theory with practical engineering examples to demonstrate how LMIs can solve complex control problems. The work progresses from fundamental concepts to advanced applications, covering topics like convex optimization, state feedback control, and robustness analysis. Real-world engineering scenarios illustrate the theoretical principles throughout each chapter, with detailed numerical examples and computational methods. The authors present both classical LMI results and newer developments in the field, including advances in semidefinite programming and interior-point methods. The text includes complete mathematical proofs alongside algorithms and computational procedures for implementing LMI-based solutions. This book serves as a bridge between abstract mathematical optimization theory and practical control engineering, demonstrating how theoretical advances in convex optimization have transformed modern control system design. Its systematic approach makes complex concepts accessible while maintaining mathematical rigor.

Readers consistently mention this book's value as a reference text for LMI optimization in control systems. Graduate students and researchers cite its clear explanations of complex concepts and practical examples. Likes: - Accessible introduction to LMI methods - Strong mathematical foundations with real-world applications - Complete coverage from basic theory to advanced topics - High-quality problem sets and exercises Dislikes: - Some sections require advanced math background - Limited coverage of recent developments (published 1994) - Physical book is expensive ($145+) - PDF formatting issues in free digital version Ratings: Goodreads: 4.29/5 (14 ratings) Amazon: 4.5/5 (4 ratings) One researcher noted: "Explains LMIs better than any other control theory text I've encountered." A graduate student mentioned: "The free PDF saved me money but has misaligned equations and poor image quality." The book remains in active use for graduate courses and research, with over 23,000 citations on Google Scholar.

Applied Linear Optimal Control by Brian Anderson and John Moore This text examines LMI-related control techniques through state-space methods and optimal control frameworks.

Convex Optimization by Stephen Boyd, Lieven Vandenberghe The book connects convex optimization theory to control systems and LMI problems with practical engineering applications.

Robust Control Design with MATLAB by Da-Wei Gu, Petko H. Petkov, and Mihail M. Konstantinov The text presents LMI-based robust control methods with computational implementations using MATLAB tools.

Linear Control Theory: Structure, Robustness, and Optimization by Hugo Pratt The work builds from linear control fundamentals to advanced LMI applications in system stability and optimization.

Nonlinear Systems: Analysis, Stability, and Control by Shankar Sastry This text extends linear matrix concepts to nonlinear control systems through Lyapunov theory and state-space methods.

🔹 The book was published in 1994 and made freely available online by its authors in 2004, demonstrating an early commitment to open access in academic publishing. 🔹 Author Stephen Boyd is a Professor at Stanford University who has won multiple IEEE awards and is cited over 220,000 times in academic literature. 🔹 Linear Matrix Inequalities (LMIs) were first used in control theory by Lyapunov in 1890, but the computational methods described in this book helped revolutionize their practical applications. 🔹 The numerical methods presented in the book formed the foundation for several popular optimization software packages, including CVX and SeDuMi. 🔹 While primarily written for control theory applications, the book's techniques have found widespread use in machine learning, statistics, and finance - particularly in portfolio optimization problems.