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Zbl 1160.93358
Karimi, H.R.; Moshiri, B.; Lucas, C.
Robust fuzzy linear control of a class of stochastic nonlinear time-delay systems. (English)
[J] Nonlinear Dyn. Syst. Theory 4, No. 3, 317-332 (2004). ISSN 1562-8353

Summary: This paper presents the fuzzy linear control design method for a class of stochastic nonlinear time-delay systems with state feedback. First, the Takagi and Sugeno fuzzy linear model is employed to approximate a nonlinear system. Next, based on the fuzzy linear model, a fuzzy linear controller is developed to stabilize the nonlinear system. The control law is obtained to ensure stochastic exponential stability in the mean-square, independent of the time-delay. The sufficient conditions for the existence of such a control are proposed in terms of a certain linear matrix inequality. Finally, a simulation example is given to illustrate the applicability of the proposed design method.

MSC 2000:: *93C42 Fuzzy control
93E03 General theory of stochastic systems
93C23 Systems governed by functional-differential equations

Keywords: Fuzzy linear control; linear matrix inequality; time-delay systems; stochastic systems; exponential stability

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Zentralblatt MATH Berlin [Germany]