The paper is focused on robust Proportional-Integral (PI) control of interval plants with gain and phase margin specifications and on the application of this approach to a Continuous Stirred Tank Reactor (CSTR). More specifically, the work aims at the determination of PI controller parameter regions, for which not only robust stability but also some level of robust performance of the closed-loop control system is guaranteed, and this robust performance is represented by the required gain and phase margin that has to be ensured for all potential members of the interval family of controlled plants, even for the worst case. The applied technique is based on the combination of the previously published generalization of stability boundary locus method (for specified gain and phase margin under the assumption of fixed-parameter plants) with the sixteen plant theorem. This extension enables the direct application of the method to design the robustly performing PI controllers for interval plants. The effectiveness of the improved method is demonstrated on a CSTR, modeled as the interval plant, for which the robust stability and robust performance regions are obtained.