Linear matrix inequalities (LMIs) have emerged as a powerful tool which has found numerous applications in many major domains of systems control, and it's getting more and more popular. This book provides a relatively systematic introduction to the basic results in LMI-based control systems analysis and design. Designed as a textbook for certain graduate and senior undergraduate courses in control systems analysis and design, it focuses on the analysis and design problems on both continuous- and discrete-time linear systems based on the LMI methods.