A synthesis of Lyapunov functions for non-linear time-varying control systems

The formulation of a class of Lyapunov functions for time-varying nonlinear control systems which occur in the stability analysis of control systems is considered. A new approach is presented, which is an extension of a generation technique for time-invariant non-linear systems. This approach, which uses by analogy the classical theory of Hamilton, permits stability and transient information to be obtained from system equations with time-varying damping as well as time-varying gain. A second and third-order example is used to illustrate the application of this new result.