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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In control theory, a control-Lyapunov function V(x,u) is a generalization of the notion of Lyapunov function V(x) used in stability analysis. The ordinary Lyapunov function is used to test whether a dynamical system is stable (more restrictively, asymptotically stable). Control theory is an interdisciplinary branch of engineering and mathematics, that deals with the behavior of dynamical systems. The desired output of a system is called the reference. When one or more output variables of a system need to follow a certain reference over time, a controller manipulates the inputs to a system to obtain the desired effect on the output of the system.