When are dynamic and static feedback equivalent?

On the K-theory of feedback actions on linear systems

“…are feedback isomorphic (see [3], [10]). This is physically realized by introducing free ancillary variables.…”

“…On the other hand we also are interested in the so-called dynamic feedback equivalence of linear systems (see [3], [9], [10] as main references). This dynamic study is based in the addition of some suitable ancillary state variables to systems [2, ch.…”

On Linear Multi-Input Systems Depending on Continuous Parameters. Feedback Equivalences in Low Dimension

“…6 We study the pointwise feedback equivalence, which is the equivalence at any point and show that this pointwise feedback equivalence is different from feedback equivalence even for simple spaces of parameters as a closed interval Λ = [a, b]. We also review local equivalence, 7 dynamic equivalence, 8 and introduce stable equivalence. We prove that all these equivalences are distinct by writing down explicit examples.…”

“…8 Thus it is not easy to find out an example of dynamic feedback equivalent linear systems that are not (global) feedback equivalent. On the contrary, one can also prove that systems are not feedback equivalent by direct calculation.…”