Stability Analysis Of Stochastic T-S Fuzzy Neural Networks

Neural network system has found widely applications in various areas such as signalprocessing, pattern recognition, automatic control, combinatorial optimization. Stability isa premise to ensure the normal operation of the system. Time delays, parameteruncertainties and stochastic perturbations which often break the stability of systems andchanges in the environment of the model. So, in this paper, based on analysis of stochasticneural networks, we shall generalize the ordinary Takagi-Sugeno(T-S) fuzzy models toexpress stochastic neural networks. The stability problem of three T-S stochastic fuzzyneural networks are considered. Main work is as follows:Firstly, the global asymptotic stability problem of stochastic neural networks withmultiple discrete time-varying delays and distributed delays is analyzed. Based on theLyapunov method and stochastic analysis approaches, the globally asymptotic stability ispresented in terms of linear matrix inequalities, then considering the same stochasticsystem, a novel linear matrix inequality(LIM)-based stability criterion is obtained by usingfuzzy rules and free weighting matrices to guarantee the asymptotic stability of the fuzzyneural networks. These criterions are looser than some existing and related results, andthrough numerical example and a simulation example shows the effectiveness of theconclusion.Secondly, the global robust stability problem of T-S fuzzy Hopfield neural networkswith parameter uncertainties and stochastic perturbations is investigated. The Lyapunovmethod and stochastic analysis approaches have been used, the globally robustasymptotically stable condition is presented in terms of linear matrix inequalities. Theresults obtained in this paper are less conservative than the ones reported so far in theliterature. A numerical example is provided to verify the effectiveness of the proposedresults.Thirdly, by utilizing the Lyapunov functional and Khasminski lemma, we analyze theglobal asymptotic stability of uncertain stochastic T-S fuzzy BAM neural networks. ALIM-based stability criterion is derived, the stochastic fuzzy neural networks is robustly, globally, asymptotically stable. Then, numerical example is given to demonstrate thecorrectness of the theoretical result.