Estimating the domain of attraction for systems with multiple non-linearities†

Abstract

The method of Lyapimov is commonly used to establish regions of attraction for non-linear systems. In some cases, by using the form of the system equations, it is possible to extend the region beyond that, given by the Lyapunov function. Willems has illustrated this technique for systems with a single non-linearity. Here it is shown that a similar approach is possible in some cases when considering systems with multiple non-linearities.

Notes

†Communicated by the Authors.