A novel methodology to solve the CQLF problem for a finite set of stable second-order systems

A new methodology to provide conclusive information about the existence/non-existence of a common quadratic Lyapunov function (CQLF) for a finite set of stable second-order systems is presented. Despite the high complexity of the CQLF problem, even in the case of N second-order systems, the results presented in this paper have a very simple and intuitive theoretical support, including topics such as classical intersection of convex sets and properties of convex linear combinations. Illustrative examples to show the performance of the proposed methodology are provided.