Extremal conitope norm methods for the control of switched systems

We describe new methods for computing the joint spectral radius and the joint spectral subradius of arbitrary sets of matrices. The methods build on two ideas previously appeared in the literature: the polytope norm iterative construction, and the lifting procedure. Moreover, the combination of these two ideas allows us to introduce a pruning algorithm which can importantly reduce the computational burden. We prove several appealing theoretical properties of our methods, and provide numerical examples of their good behaviour.