Design of Delay-Dependent Exponential Estimator for T–S Fuzzy Neural Networks with Mixed Time-Varying Interval Delays Using Hybrid Taguchi-Genetic Algorithm

Abstract

This paper considers the design of state estimator for Takagi---Sugeno (T---S) fuzzy neural networks with mixed time-varying interval delays. The mixed time-delays that consist of both the discrete time-varying and distributed time-delays with a given range are presented. The activation functions are assumed to be globally Lipschitz continuous. By using the Lyapunov-Krasovskii method, a linear matrix inequality (LMI) approach is developed to construct sufficient conditions for the existence of admissible state estimator such that the error-state system is exponentially globally stable. To avoid complex mathematical derivations and conservative results, a new hybrid Taguchi-genetic algorithm method is integrated with a LMI method to seek the estimator gains that satisfy the Lyapunov-Krasovskii functional stability inequalities. The proposed new approach is straightforward and well adapted to the computer implementation. Therefore, the computational complexity can be reduced remarkably and facilitate the design task of the estimator for T---S fuzzy neural networks with time-varying interval delays. Two illustrative examples are exploited in order to illustrate the effectiveness of the proposed state estimator.