On the relationship between matrix pencil eigenvalue criteria and the choice of Lyapunov function for the analysis of second order switching systems

In this paper we present sufficient conditions for the stability of a class of switching systems. These results are of interest for two reasons. First, the conditions presented are matrix pencil eigenvalue criteria, and are therefore coordinate independent and easily verifiable, and may generalise to high order switching systems. Next, more importantly, we show a direct relationship between the form of our criteria and the choice of Lyapunov function used to demonstrate stability (quadratic or otherwise). Extension of these statements to higher order systems are currently being investigated.