Maximization of the volume of the μ guaranteed stability domain using Particle Swarm Optimization

The robustness against parametric uncertainties can be studied using the structured singular value μ. In that case, a normalization of the uncertain parameters is performed, and the μ analysis provides the larger parallelepiped centered in the nominal and included in the stability domain. However, results depend on the initial normalization. In this paper, the normalization is optimized so as to get the largest guaranteed stability domain. The corresponding problem being highly nonlinear, a metaheuristic method, Particle Swarm Optimization, is used for that purpose. An academic and a real life examples are used to prove the viability of the approach.