ON THE GAP BETWEEN THE STRUCTURAL CONTROLLABILITY OF TIME-VARYING AND TIME-INVARIANT SYSTEMS

We compare structural controllability of time-invariant and time-varying systems when the input control sequences have a restricted length k. The dimension of controllable space coincide in the following three special cases: the input sequences have length k = 2, the input sequences have length k = n where n is the size of the system (i.e., the ultimate controllability is the same in both cases), for every length of input sequences provided that the system has a single input only. On the other hand, we prove that there may appear a gap for every input length k such that 2 < k less-than-or-equal-to n/2. The case when n/2 < k < n is left open.