Comments on “Optimally switched linear systems”

The technical note titled “Optimally switched linear systems” by the authors T. Das and R. Mukherjee addresses the problem of optimal switching for switched systems. The proof of the theorem in the paper is incorrect and point out an important theoretical point which explains why the optimal switched solution does not exist whenever there exists a singular one to a relaxed problem. This point has also important consequences concerning numerical difficulties encountered in solving such problems and are also discussed.