ABSTRACT
Lyapunov functions represent the primary tool for the stability analysis of nonlinear systems. They verify the stability of a given trajectory, and they also provide an estimate of its region of attraction. The purpose of this text is to illustrate the utility of Lyapunov functions in the synthesis of nonlinear control systems. We will focus on recursive state-feedback design methods which guarantee robust stability for systems with uncertain nonlinearities. Lyapunov design is used inmany other contexts, such as dynamic feedback, output feedback, gain assignment, estimation, and adaptive control, but such topics are beyond the scope of this chapter.
