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Preface

This book will discuss Linear Matrix Inequalities in Control Systems. The recent introduction of Linear Matrix Inequality (LMI) methods in control has dramatically expanded the types and complexity of the systems we can control.

For example, consider the problems: Gain Scheduling for Missile Attitude Control (A switched system); Control of Robots over Noisy Communication Channels (sampled-data systems); Remote Control of Spacecraft Attitude (a delayed system); Behavioral Therapy (A system with binary inputs); or self-driving vehicles (a case of decentralized control). None of these systems can be studied using classical root-locus or PID control methods. Rather, advances in these fields have been made possible through the increased power and flexibility created by the LMI (optimization-based) approach to control.

The objective of this book is to let readers be able to use LMI solvers to synthesize optimal or suboptimal controllers and estimators for multiple classes of state-space systems. This book will require prior knowledge of linear algebra, integral and differential calculus, and at least some exposure to ordinary differential equations. Some background in control systems is also preferrable. In addition, a prior knowledge of integral transforms, specifically the Laplace transforms will be very beneficial. Access to MATLAB is also required, including the robust control toolbox. A guide on the installation and usage of software used in LMI and Optimization is given in this book. Use the links below for the reference on Control systems and transformation of Matrices.