This two-part paper presents general methodologies for the evaluation of passive compressor stabilization strategies using tailored structural design and aeromechanical feedback control (Part I), and quantitatively compares the performance of several aeromechanical stabilization approaches which could potentially be implemented in gas turbine compression systems (Part II). Together, these papers offer a systematic study of the influence of ten aeromechanical feedback controllers to increase the range of stable compressor operation, using static pressure sensing and local structural actuation to postpone modal stall inception. In this part, the stability of aeromechanically compensated compressors was determined from the linearized structural-hydrodynamic equations of stall inception. New metrics were derived, which measure the level of aeromechanical damping, or control authority of aeromechanical feedback stabilization. They indicate that the phase between the pressure disturbances and the actuation is central to assess the impact of aeromechanical interactions on compressors stability.