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.