Abstract
The derivation of tight eigenvalue inclusion regions help extend the Generalised Nyquist criterion to the case of uncertain systems and lead to a necessary and sufficient Nyquist type of criterion for the case of unstructured perturbations. The approach provides an exact and immediate assessment of gain/phase margins. When applied to systems with nonlinearities which are sector bounded but otherwise unstructured, it produces a necessary and sufficient test for the circle criterion conditions to hold in the multivariable case; as such the resulting criterion is an improvement on the currently available extensions of the circle criterion.
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