Regions of stability for gain or phase variations in multivariable systems

This paper extends the well-known norm-bounded robust stability criteria from strict inequalities that specify open sets to inequalities that specify closed sets. Both the Nyquist and inverse Nyquist type of norm-bounded criteria are considered. The extended criteria form the theoretical basis in the formulation of an iterative procedure for searching the regions of stability for simultaneous gain or phase variations in multivariable feedback systems. The basic idea of the iterative procedure lies in successively perturbing the feedback system from a set of nominal gains or phases that are on the boundary of a previously established region of stability. The iterative procedure is illustrated by a numerical example.