Numerical Computations of Lyapunov Functions for Switched Linear Systems

We compare different optimisation methods for the computation of Lyapunov functions for switched linear systems. In particular, we compare methods based on linear programming to methods based on semi-definite optimisation. For the linear programming methods, we describe two approaches aimed at reducing the size of the linear programme. This is done by using different kinds of coordinate transforms. One attempts to increase the rotational symmetry of the solution trajectories of the sub-systems. The other one rotates the areas of maximum curvature of possible Lyapunov functions to where the triangulation is closer meshed. We investigate the effect of these coordinate transforms on several examples and compare their efficiency.