Generalized short circuit ratio (gSCR) for grid strength assessment of multi-infeed high-voltage direct current (MIDC) systems is a rigorous theoretical extension of the traditional SCR, which enables SCR to be extended to MIDC systems. However, gSCR is originally based on the assumption of homogeneous MIDC systems, in which all high-voltage direct current (HVDC) converters have an identical control configuration, thus presenting challenges to applications of gSCR to inhomogeneous MIDC systems. To weaken this assumption, this paper applies matrix perturbation theory to explore the possibility of utilization of gSCR into inhomogeneous MIDC systems. Results of numerical experiments show that in inhomogeneous MIDC systems, the previously proposed gSCR can still be used without modification. However, critical gSCR (CgSCR) must be redefined by considering the characteristics of control configurations of HVDC converter. Accordingly, the difference between gSCR and redefined CgSCR can effectively quantify the pertinent AC grid strength in terms of the static-voltage stability margin. The performance of the proposed method is demonstrated in a triple-infeed inhomogeneous line commutated converter based high-voltage direct current (LCC-HVDC) system.