The area of hybrid dynamical systems (HDS) represents a difficult challenge to control engineers and is referred to as the control theory of tomorrow due to its future potential for solving problems. This relatively new discipline bridges control engineering, mathematics and computer science. There is now an emerging literature on this topic descibing a number of mathematical models, heuristic algorithms and stability criteria. This text focuses on a comprehensive development of HDS theory and integrates results established by the authors. The work is a self-contained text/reference covering several theoretically interesting and practically significant problems concerning the use of switched controllers. Also under examination is the sensor scheduling problems. The emphasis is on classes of uncertain systems as models for HDS. The volume: focuses on the design of robust hybrid dynamical systems in a logical manner; provides extensive coverage of dynamic programming concepts; applies hybrid control systems framework to two classical robust control problems (design of an optimal stable controller for a linear system and simultaneous stabilization of a collection of plants); presents a detailed treatment of stability and H-infinity problems; covers recent original results with complete mathematically rigorous proofs. Researchers and postgraduate students in control engineering, applied mathematics and theoretical computer science should find this book covers the latest results in this area of research; and advanced engineering practitioners and applied researchers working in areas of control engineering, signal processing, communications and fault detection should also find it an up-to-date resource.