A applicability of decomposed fuzzy structures for modeling and control of non-linear dynamic systems based on fuzzy relational models is proposed in this lecture. The basic idea is a concept supported by the decomposition of multivariable rule base. The set of decomposed fuzzy models based on the simplified inference break up method are proposed and applied to a dynamic systems modeling. Identification algorithms based on fuzzy relational matrices and the neural network identification based on back-propagation learning are applied. A comparative study of the dynamic system identification with the conventional relational model and the decomposed relational model is presented for Box-Jenkins data. The decomposed PID fuzzy logic controller (PID-FLC) has proportional, integral and derivative separate parts with their own rule bases. The real-world example of controlling a simple magnetic suspension system - iron ball levitation control in the magnetic field of the electromagnet - demonstrates the applicability and benefits of decomposed PID-FLC, namely a significantly reduced number of rules. A comparative study of the decomposed PID-FLC and PID controller is presented.