Sparse static output feedback controller design via convex optimization

We consider the problem of designing a stabilizing static output feedback controller subject to a pre-specified sparsity pattern. While this problem is known to be NP-hard, our main result shows that a sequence of convergent convex relaxations can be obtained by recasting the problem into a polynomial optimization through the use of polyhedral Lyapunov functions. Moreover, as shown in the paper, combining these ideas with rank minimization tools leads to a computationally attractive algorithm. These results are illustrated with an example, where we show the effectiveness of the proposed approach vis-a-vis existing techniques.