Common Quadratic Lyapunov Functions for Sets of Second-Order Linear Systems: A Simple Graphical Criterion

This letter presents a simple graphical criterion to obtain all common quadratic Lyapunov functions for nonlinear systems contained in the convex-hull of a set of second-order linear time-invariant systems. It simply consists in finding the intersection between the interior of some ellipses. The proposed criterion is declined for both continuous-time and discrete-time systems and is illustrated by numerical examples.