Stability Analysis of Real - Time Systems :

Both crisp and fuzzy rule-based expert systems are increasingly used in the real-time environments. For both types of systems the stability and nite response time are required. It is therefore crucial for both to provide tools that perform stability analysis. This paper shows how the analysis tools built for crisp real-time rule-based system might be used for fuzzy systems as well. Major diierence of the two are crisp/fuzzy interpretation of variables and operations on them, and sequen-tial/parallel interpretation of rule ring. We propose an analysis method that takes a fuzzy system and extends it with rules that account for the diierence of the results of parallel and sequential ring. An extended system can then be analyzed with the tools that rely on sequential rule-ring interpretation. In addition, we show that only minor changes of crisp stability analysis tools are necessary to enable their use for such extended fuzzy systems.