Convex synthesis of symmetric modifications to linear systems

We develop a method for designing symmetric modifications to linear dynamical systems for the purpose of optimizing ℋ₂ performance. For systems with symmetric dynamic matrices this problem is convex. While in the absence of symmetry the design problem is not convex in general, we show that the ℋ₂ norm of the symmetric part of the system provides an upper bound on the ℋ₂ norm of the original system. We then study the particular case where the modifications are given by a weighted sum of diagonal matrices and develop an efficient customized algorithm for computing the optimal solution. Finally, we illustrate the efficacy of our approach on a combination drug therapy example for HIV treatment.