This paper develops a fuzzy controller design method via estimated state feedback scheme for discrete-time nonlinear stochastic time-delay systems which are presented by Takagi– Sugeno fuzzy model with multiplicative noises. The proposed design method is accomplished by the concept of parallel distributed compensation. Using the Lyapunov-Krasovskii function and passivity theory, the stability conditions are derived to guarantee the stability and attenuation performance. An algorithm is proposed in this paper to solve the derived stability conditions that belong to non-strict linear matrix inequality problems. Moreover, the discrete Jensen inequality and free-weighting matrix technique are employed to decrease the conservatism of the proposed design method. Finally, the control of a nonlinear time-delay pendulum system is provided to illustrate the effectiveness and usefulness of the proposed fuzzy control method.

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