Although LMI has emerged as a powerful tool with applications across the major domains of systems and control, there has been a need for a textbook that provides an accessible introduction to LMIs in control systems analysis and design. Filling this need, LMIs in Control Systems: Analysis, Design and Applications focuses on the basic analysis and design problems of both continuous- and discrete-time linear systems based on LMI methods. Providing a broad and systematic introduction to the rich content of LMI-based control systems analysis and design with applications, this book is suitable for use as a textbook for LMI related courses for senior undergraduate and postgraduate students in the fields of control systems theory and applications. Key Features: Contains four well-structured parts: Preliminaries, Control Systems Analysis, Control Systems Design, and Applications, as well as an introduction chapter and two appendices Summarizes most of the technical lemmas used in the book in one preliminary chapter, and classifies them systematically into different groups Includes many examples, exercises, and practical application backgrounds Summarizes most of the important results in the last section of each chapter, in a clear table format Contains an application part composed of two chapters that respectively deal with missile and satellite attitude control using LMI techniques Provides a brief and clear introduction to the use of the LMI Lab in the MATLAB® Robust Control Toolbox Supplies detailed proofs for all main results, with lengthy ones clearly divided into different subsections or steps—using elementary mathematics whenever possible Uses a pole assignment Benchmark problem, in support of the numerical reliability of LMI techniques, where numerical unreliability could result in a solution to a problem that is far from the true one A Solutions Manual and MATLAB® codes for the computational exercise problems and examples are available upon qualified course adoption.