Decentralized computation for robust stability analysis of large state-space systems using Polya's theorem

In this paper, we propose a parallel algorithm to solve large robust stability problems. We apply Polya's theorem to a parameter-dependent version of the Lyapunov inequality to obtain a set of coupled linear matrix inequality conditions. We show that a common implementation of a primal-dual interior-point method for solving this LMI has a block diagonal structure which is preserved at each iteration. By exploiting this property, we create a highly scalable cluster-computing implementation of our algorithm for robust stability analysis of systems with large state-space. Numerical tests confirm the scalability of the algorithm.