Determination of stability regions with the inverse Nyquist array

A new criterion for closed-loop stability and the design of linear multivariable control systems is developed using the inverse-Nyquist-array method and an Ostrowski theorem. Estimates of the gain margins in each loop and bounds on the stable-gain space are obtained using the bands of Ostrowski circles superimposed on the diagonal elements of the inverse Nyquist array. The manner of application of this new approach is similar to the way in which the bands of Gershgorin circles are used. The new criterion allows the diagonal dominance requirements to be relaxed in one row or in one column of the inverse Nyquist array at each point on the D contour, while still permitting the origin encirclements of the determinant of the inverse-transfer-function matrix to be determined from those of its diagonal elements. As a consequence the estimated stability region is larger than that obtained when strict dominance requirements are imposed.