Approximation of extreme measure for switched linear systems

For continuous-time switched linear systems, the largest divergence rate is characterized by the least possible matrix set measure (extreme measure) of the subsystems. However, how to compute the value is still an unsolved problem. In this note, an algorithm based on the sum-of-squares (SOS) technique is introduced to approximate the switched system´s extreme measure by solving a generalized eigenvalue problem. It explores a way to approximate the extreme measure of continuous-time switched linear systems.