New Approaches to Fuzzy Modeling and Control - Design and Analysis

Stability Conditions of Fuzzy Filter Type III

“…The Figure 2 shows the fuzzy filter structure:The FDF interacts with an external reference model (real process) changes and the filter will selects the best answer to approximate the signal with minimum error. Then, the fuzzy filter has next stages [21]: The fuzzy filter initially has the classification of the reference process model conditions as operation levels; having the knowledge of all the possible levels. constitute an automatic updating selection to follow the best condition of a process.…”

Open Cyber-Architecture for electrical energy markets

“…A problem of fundamental importance is the stability of the large scale system in the presence of fuzzy constraints. For Mamdani systems the approach of [34] provides an excellent methodology based on Lyapunov stability theory. For TS systems the stability problem was reviewed by Sugeno in [35] and most of the results available require a common Lyapunov function in all regions of operation.…”

“…This severe restriction was removed using a Lyapunov approach by Sonbol and Fadali for the discrete time [36] and continuous time [37] cases. A combination of the approaches of [34] and [37] is needed to analyze the stability of large scale systems with fuzzy rule constraints.…”

“…The results of [34] also offer an attractive approach to fuzzy system optimization that can be extended to large-scale systems with fuzzy rule constraints and used in the analysis of the smart grid. The approach uses the hyperbolic model …”

“…The optimal solution is in the form u = Hy, where H is an m by n constant matrix. However, Margaliot et al [34] do not consider the effect of fuzzy rule constraints on their design. Neither do they consider the case of a decentralized large-scale system.…”