Stabilization of Nonlinear Systems by Switched Lyapunov Function

If a Lyapunov function is known, a dynamic system can be stabilized. However, computing a Lyapunov function is often challenging. This paper takes a new approach; it assumes a basic Lyapunov-like function then seeks to numerically diminish the Lyapunov value. If the control effort would have no effect at any iteration, the Lyapunov-like function is switched in an attempt to regain control. The method is tested on four simulated systems to give some perspective on its usefulness and limitations. A highly coupled 3rd order system demonstrates the approach’s general applicability and finally the coordinated control of 7 motors for a robotic application is considered. Details on the publicly available software packages for application agnostic software and hardware environments are also presented.