ABSTRACT
The chapter presents a conceptual development of vector Lyapunov functions by introducing (semi-) definite vector functions and related various kinds of vector Lyapunov functions. They enable us to extend the Lyapunov method without using a scalar Lyapunov function. Besides, they permit synthesis of robust control of airplanes and other nonlinear systems incorporating all mechanical systems with a variable mass and/or loads (e.g., robots, ships, spacecrafts) to guarantee a high-quality output tracking together with an appropriate Lyapunov stability of a desired motion.
