Abstract
This paper investigates new criteria of the robust $$H_\infty $$Hź stability for a class of uncertain stochastic fuzzy mixed-delay systems with nonlinear noise disturbances by employing an improved free-weighting matrix approach. The fuzzy system is based on the Takagi---Sugeno model that is often used to represent the complex nonlinear systems in terms of fuzzy sets and fuzzy reasoning. To reflect more realistic dynamical behaviors of the system, both the parameter uncertainties and stochastic disturbances are considered, the stochastic disturbances are given in the form of a Brownian motion. The mixed delays comprise both discrete and distributed time-varying delays. In terms of a stochastic fuzzy Lyapunov functional, a sufficient criterion is proposed to investigate dynamical behaviors of the system in the mean-square sense with an $$H_\infty $$Hź performance index.
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