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This paper focuses on stability of automotive supervisory control systems (ASCSs). It serves to introduce the concept of stability with respect to an entire ASCS. The realm of ASCSs is categorized and a brief description of pre-existing classical methods of stability analysis is presented. With the concept then having been fully introduced, an approach to evaluating stability of a key category of ASCS, the rule-based deterministic ASCS, is presented. This approach, cited from unrelated modern literature concerning stability of deterministic finite state machines, is novel in that its original target research area was not specifically automotive engineering.