Iterative Greedy LMI for Sparse Control

In this letter, we propose a novel method to find matrices that satisfy sparsity and LMI (linear matrix inequality) constraints at the same time. This problem appears in sparse control design such as sparse representation of the state feedback gain, sparse graph representation with fastest mixing, and sparse FIR (finite impulse response) filter design, to name a few. We propose an efficient algorithm for the solution based on Dykstra's projection algorithm. We then prove a convergence theorem of the proposed algorithm, and show some control examples to illustrate merits and demerits of the proposed method.

Automated summary

In this letter, a novel method is proposed to find matrices that satisfy both sparsity and LMI constraints at the same time. The method is applied in sparse control design and an efficient algorithm based on Dykstra's projection algorithm is introduced. A convergence theorem of the proposed algorithm is proven and some control examples are presented to illustrate the merits and demerits of the method.