This book is concerned with the problem of quadratic guaranteed cost control for linear uncertain systems. Quadratic guaranteed cost control is a methodology for the design of quadratically stabilizing controllers which assure a guaranteed level of performance for the closed loop system. In this book, both the Algebraic Riccati Equation approach and the Linear Matrix Inequality approach are applied to problems of constructing optimal or sub-optimal quadratic guaranteed cost controllers for different classes of uncertain systems. The systems under consideration are linear uncertain systems with structured or unstructured uncertainties and linear uncertain systems with time-delays. The problem of quadratic guaranteed cost control together with robust pole placement is also considered for linear uncertain systems.