An algorithm for common quadratic Lyapunov function

Using Lyapunov mapping, in this paper a necessary and sufficient condition for a set of linear systems to share a common quadratic Lyapunov function is presented. Based on this condition an algorithm has been developed to search such a Lyapunov function. Theoretical proof for the executability of the algorithm is completed. The algorithm has been coded as a software, which shows the algorithm is very powerful. Several numerical examples, that are produced by the software, are presented to support the algorithm.