Characterization of the Hurwitz Region for Systems with Parametric Uncertainty

The paper considers stability issues for linear, time-invariant, single-input, multi-output systems which are affected by parametric uncertainty. Our objective is to completely characterize in parameter space, the stability region of a system for a given feedback compensator that stabilizes the nominal part. It is shown that in the case when parameters affect the closed loop characteristic polynomial in a linear manner, this region is the intersection of two sets. One is generated by a finite number of linear constraints. The other in general has a nonlinear boundary (in parameter space) which can be expressed as a function of frequency. It is also shown that if certain shaping conditions are satisfied the stability region is generated solely by a finite number of linear constraints.