Lagrange Stability for T–S Fuzzy Memristive Neural Networks with Time-Varying Delays on Time Scales

Abstract

The existed results of Lagrange stability for neural networks (NNs) are scale-free, and hence, conservativeness appears naturally. A class of Takagi–Sugeno (T–S) fuzzy memristive NNs (FMNNs) with time-varying delays is considered on time scales. First, a class of FMNNs is formulated using characteristics of memristors and T–S fuzzy rules. Then some new scale-limited criteria of global exponential stability in Lagrange sense are obtained for FMNNs with bounded feedback functions on the basis of inequalities on time scales and inequality scaling techniques. Also, novel criteria for Lurie-type feedback functions are given, which mainly employ the constructed scale-limited generalized Halanay inequality. Moreover, by matrix-norm strategies, some matrix-norm-based scale-limited criteria are derived for bounded and Lurie-type feedback functions, respectively. It also can be seen that the matrix-norm-based criteria are in accordance with the matrix-measure-based conditions provided the time scale is specified as real set. All scale-limited criteria for Lagrange stability not only include continuous-time criteria and its discrete-time analogues, but also contain more complex cases such as the arbitrary combination of them. In the end, some numerical simulations exhibit the validity of the obtained results.