Robust stability: A relaxation method for the generation of polyhedral Lyapunov functions

In this paper we consider the robustness analysis problem for linear continuous-time systems subject to parametric time-varying uncertainties, making use polyhedral Lyapunov functions. In the literature it has been shown that the class of polyhedral functions is universal for the robust stability problem, while, for instance, the class of quadratic functions is not. This fact justifies the effort of developing efficient algorithms for the construction of optimal polyhedral Lyapunov functions. In this context, we provide a novel convex condition for the construction of a polyhedral Lyapunov function. Finally, to show the effectiveness of the method, we consider a numerical problem that represents a sort of benchmark for the robust stability analysis.