Given a certain class of regular spectral systems, an algorithm is presented that is designed to test the stability properties of the feedback interconnection of such a system and either a bounded state-feedback operator or a finite-dimensional linear time-invariant controller. The applicability of this test is independent of the method used to design the feedback controller, and is designed to provide a separate, independent method for verifying whether or not the plant-controller interconnection is exponentially stable. The test is particularly well suited to problems involving certain partial differential equations (PDE) with spatially varying coefficients or complicated boundary shapes.