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1. Introduction
In recent years, there has been an increasing interest in the fuzzy control of nonlinear systems. Some works have studied the stability and the stabilization of closed-loop fuzzy systems. Specially, these approaches are studied for the T-S fuzzy models which are described by a set of fuzzy “IF-THEN” rules with fuzzy sets in the antecedent and dynamic systems in the consequent part. The subsystems are considered as local linear models, the aggregation of which representing the nonlinear systems. Tanaka and Sugeno [1] presented sufficient conditions for the stability of T-S models. Applying the fuzzy modeling approach, many papers [2–4] have been proposed to investigate the controller design methods of nonlinear systems. According to the discrete T-S fuzzy models, the stability analysis and synthesis have been considered in [5–9]. Not only control schemes [5–8] but also filter design methods [9] have been proposed for nonlinear discrete-time systems via T-S fuzzy model. In general, the stochastic signals and random parameters may exist in the real systems. It is interesting to consider the stochastic behaviors for analyzing the stability of nonlinear stochastic systems. Recently, the T-S fuzzy system with multiplicative noise term [10–16] is structured for representing the nonlinear stochastic system. In [10, 11, 13, 15], the time delay phenomenon is considered in the control problem. Besides, the fuzzy filter design problem for nonlinear stochastic systems is studied in [12]. Different from the traditional additive noise, multiplicative noise is more practical since it allows the statistical description of the noise to be unknown a prior but depends on the control and state solution. Therefore, the T-S fuzzy model with multiplicative noises is considered in this paper to represent the nonlinear stochastic systems.
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