On the generalized Nyquist stability criterion

This paper starts with a straightforward self-contained treatment of the generalized Nyquist stability criterion based on the eigenloci of the open-loop transfer function matrix. The derivation is straightforward and does not invoke algebraic function theory, branch cuts and Riemann surfaces. A similar criterion is derived for the distributed case where the open-loop transfer function matrices belong to the recently proposed algebra B(σo)m×m 9,14. This leads to a new graphical stability test based on eigenloci which applies to distributed, possibly unstable, open-loop transfer functions.