Qualitative modeling is one promising approach
to the solution of difficult tasks automation if qualitative process models are not available. This contribution presents a new concept of qualitative dynamic process
modeling using so called Dynamic Adaptive Neuro fuzzy Systems. In contrast to common approaches of Adaptive Neuro Fuzzy modeling [1], the dynamic system is completely described in the neuro fuzzy domain: the neuro fuzzy information about the previous state is directly applied to compute the system’s current state, i.e. the delayed neuro fuzzy output is feedback to the input without
defuzzification. Knowledge processing in such dynamic neuro fuzzy systems requires a new inference method, the inference with interpolating rules. This yields the framework of a new systems theory the essentials of which are given in further section of the paper. First, an identification method is presented, using a combination of
linguistic knowledge. Next, a stability definition for dynamic neuro fuzzy systems as well as methods for stability analysis is given. Finally, a neuro fuzzy
model-based neuro fuzzy controller design method is developed. The identification of real problems and neuro fuzzy controller design for inverted pendulum system
demonstrate the significance of the new systems theory.