The Boundary Behavior of the Nyquist Map
- The crucial issue of fast robust stability test is whether the
Nyquist map and the boundary commute in the sense that:
- If the Nyquist map commutes with the boundary, then we can generate
the entire boundary of the image by just sweeping the boundary of the
domain. We can then easily apply the Nyquist Stability Criterion
- On the other hand, if the above property is not satisfied, we
need to search inside the domain of the Nyquist map in order to
generate its image, increasing the complexity of the problem by orders
of magnitude
- Unfortunately, most of the robust stability problems do not
satisfy the above relation
- In this reasearch we use the simplicial approximation theorem
implemented using computational geometry techniques, to generate a fast and
reliable way of checking the system stability whenever the above
property is not satisfied
