Further results on controllability of linear systems with switching delays ?

We prove two more results on controllability of LTI systems with switching delays. Firstly, we improve our previous results on controllability verification (when arbitrarily large look-ahead of the switching signal is allowed) by providing an algorithm which is not restricted to regular matrices. In particular we provide a more detailed analysis for nihilpotent matrices (i.e. matrices with only zero eigenvalues): we restate this problem as a completely combinatorial one and provide a polynomial time algorithm, which has much better efficiency than a naive brute force algorithm. Secondly, we show that when the switching signal cannot be measured it can be necessary to use nonlinear controllers for stabilizing a linear plant.