Stability and stabilizability of fuzzy-neural-linear control systems

This paper discusses stability analysis of fuzzy-neural-linear (FNL) control systems which consist of combinations of fuzzy models, neural network (NN) models, and linear models. The authors consider a relation among the dynamics of NN models, those of fuzzy models and those of linear models. It is pointed out that the dynamics of linear models and NN models can be perfectly represented by Takagi-Sugeno (T-S) fuzzy models whose consequent parts are described by linear equations. In particular, the authors present a procedure for representing the dynamics of NN models via T-S fuzzy models. Next, the authors recall stability conditions for ensuring stability of fuzzy control systems in the sense of Lyapunov. The stability criteria is reduced to the problem of finding a common Lyapunov function for a set of Lyapunov inequalities. The stability conditions are employed to analyze stability of FNL control systems. Finally, stability analysis for four types of FNL control systems is demonstrated.