A new robust stability criterion for linear and non-linear multivariable feedback systems

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Abstract
Earlier eigenvalue inclusion regions are replaced by new regions which are tight and thus lead to sufficient and necessary stability conditions for uncertain linear multivariate systems in the presence of unstructured perturbations. The approach provides an exact and immediate assessment of gain and phase margins. When applied to systems with sector bounded but unstructured non-linearities, the inclusion regions produce a necessary and sufficient test for the circle criterion conditions to hold in the multivariable case; as such the resulting stability criterion gives the best possible Nyquist-type extension of the circle criterion to the multivariable case for unstructured non-linearities.