Observer-based control for state estimation of uncertain fuzzy neural networks with time-varying delay

By ordinary Takagi-Sugeno (TS) fuzzy models, complex nonlinear systems can be represented to a set of linear sub-models by using fuzzy sets and fuzzy reasoning. This paper is concerned with the problem of observer-based state estimation for fuzzy neural networks (FNNs) with time-varying structured uncertainties and time-varying delay. The problem addressed is to estimate the neuron states, through available output measurements, such that the dynamics of the estimation error is globally exponentially stable. An effective linear matrix inequality approach is developed to solve the neuron state estimation problem. In particular, we derive the conditions for the existence of the desired estimators of the delayed neural networks for all admissible parametric uncertainties. The designed controller simultaneously contains both the current state information and nonlinear disturbances on the network outputs and can be derived by solving a linear matrix inequality (LMI). A numerical example is included to illustrate the applicability of the proposed design method.