An introduction to Lyapunov's second method

A general procedure for investigating stability of many sorts of dynamic systems is the second method of Lyapunov, which uses only the form of equations describing the system, without requiring explicit knowledge of their solutions. Its application to a given system requires determination of a special Lyapunov function which, for a stable system, is itself positive but has a negative time-derivative. This function also may yield certain information regarding the transient response. Discussion of the basic principle of the method is given, along with illustrative applications to a few simple cases.