Computation of linear comparison equations for stability analysis of interconnected systems

Sum-of-squares (SOS) methods have been shown to be very useful in computing polynomial Lyapunov functions for systems of reasonably small size. However for large scale systems it is necessary to use a scalable alternative using vector Lyapunov functions. Earlier works have shown that under certain conditions the stability of an interconnected system can be studied through suitable comparison equations. However finding such comparison equations can be non-trivial. In this work we propose an SOS based systematic procedure to directly compute the comparison equations for interconnected system with polynomial dynamics. With an example of interacting Van der Pol systems, we illustrate how this facilitates a scalable and parallel approach to stability analysis.