Application of the QE Method to a Common Infinity Lyapunov Function Problem for Continuous Systems

Abstract

This report introduces application results of QE method to common infinity (l_∞) Lyapunov function problem for continuous-time linear time-invariant systems. First, the report presents an application of QE method to find the existence condition of a common l_∞ Lyapunov function for a set of continuous-time linear time-invariant systems and gives a numerical example of a pair of second order systems. Next, by giving numerical examples, the report makes clear about the non-inclusion and non-exclusion relation between the existence conditions of common l_∞and l₂ Lyapunov functions for a pair of second order continuous-time linear time-invariant systems.