An LMI-Based Method for H2/H∞ Control Design under Sparsity Constraints

H2 and H∞ based control design methodologies are widely used to deal with multivariable control problems. In general, however, finding a norm-minimizing controller subject to a structural constraint is not a convex optimization problem, and in many cases is intractable. In this paper we propose an LMI based solution to some H2/H∞ specific design cases where the controller satisfies a quadratic invariance property with respect to the controlled system. The proposed method can be applied indifferently on stable or unstable systems. The problem of Lower Block Triangular (LBT) H2/H∞ controller design is considered as a particular case. Finally, an application to the control of a platoon of vehicles problem and a comparison with some existing methods is given.