This textbook provides an accessible introduction to linear matrix inequalities (LMIs) that requires no prior knowledge of the subject. It covers both the theoretical foundations and practical applications for solving real-world control problems using MATLAB, beginning with the basic introduction “My First LMI” and gradually progressing to more advanced control challenges. Essential background information on dynamic systems analysis and linear algebra is included, specifically tailored for applications in LMI-based control. Readers will learn about system stability and stabilization through an intuitive explanation of the Lyapunov energy function and its connection to LMI formulations. The core content addresses major control design problems for both continuous-time and discrete-time linear time-invariant (LTI) systems. Additionally, extensions to output feedback and linear parameter-varying (LPV) control are discussed. The theoretical foundations are complemented by practical, challenging design problems that highlight the real-world applicability of LMIs through experimental implementation on platforms such as a 3-DOF helicopter and an active suspension system. 

Robust and Optimal Controller Design via Linear Matrix Inequalities provides a well-structured learning experience, empowering a new generation of students, practicing engineers, and researchers to confidently adopt and apply LMIs in both academic and industrial control applications.

Edvaldo Assunção, Ph.D., is an Associate Professor in the Department of Electrical Engineering with the School of Engineering at São Paulo State University (UNESP). He received his Bachelor’s degree from the School of Engineering at São Paulo State University (UNESP), his Master’s degree from the Aeronautics Institute of Technology (ITA-CTA), and his Ph.D. from the University of Campinas (UNICAMP) all in Electrical Engineering in 1989, 1991, and 2000, respectively. He was awarded the São Paulo Engineering Institute Prize for Best Graduate Student of the Year in 1989 at UNESP. Professor Assunção is renowned for his inspiring teaching spirit, which has motivated hundreds of students over 30 years of dedication to engineering classes, especially in linear control. He has also earned national and international recognition for his research in control systems, having published over 100 research articles focusing mainly on topics such as control theory and applications, LMI-based designs, and optimal robust control.

Bruno Sereni, Ph.D., is an Assistant Professor with the Faculty of Engineering, Architecture, Urbanism, and Geography (FAENG) at the Federal University of Mato Grosso do Sul (UFMS). He received his Bachelor’s, Master’s, and Ph.D. degrees in Electrical Engineering from São Paulo State University (UNESP), School of Engineering, in 2017, 2019, and 2023, respectively. He graduated as the top student in his undergraduate class at UNESP. Since 2019, he has been conducting research in linear control of linear parameter-varying systems, H-infinity control, and stabilization of linear systems via static output feedback using linear matrix inequalities. Since an early age, Professor Sereni has demonstrated a natural vocation for teaching, marked by a genuine enthusiasm for knowledge sharing and a remarkable ability to communicate complex ideas with clarity. He is recognized for his patience and dedication in meticulously preparing didactic materials for his courses, all of which are designed to make abstract concepts accessible and engaging for his students. His teaching practice reflects a continuous commitment to pedagogical excellence and student-centered learning.