Robust control under parametric uncertainty via primal-dual convex analysis

A numerical method is proposed for optimal robust control synthesis. The method applies to the case when the coefficients of the characteristic polynomial depend linearly on the uncertain parameters. A primal/dual pair of infinite-dimensional convex problems is solved by successive finite-dimensional approximations. The primal/dual pair has no duality gap, and both upper and lower bounds produced by the approximations converge monotonically to the optimal value. Keywords—robust stabilization, parametric uncertainty, convex optimization, duality, finite dimensional approximation