On structural, number theorectic and fuzzy relational properties of large multi-conneced systems of feedback fuzzy state models (FFSSM's)

Abstract

Large systems consist of many functional components. The interconnectivity of the components determines the output performance of large complex systems. In the current study, a detailed treatise on a multi-connected feedback fuzzy state space model (FFSSM) of a dynamical system is given. The concept of a single FFSSM is generalized to a large connected system of FFSSM. The convexity and normality of the induced solution of a single FFSSM helps generalize these properties to large connected systems of FFSSM. Likewise, the application of the Modified Optimized Defuzzified Value Theorem and Extended Modified Optimized Defuzzified Value Theorem help in deriving two important theorems for determining the optimal inputs in multi-connected systems of FFSSM. The BIBO stability of the multi-connected system of FFSSM’s is also studied. Another two important parts of the study are the application of the number theoretic concepts and fuzzy relational calculus in the study of the physical properties of the FFSSM’s.