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The passivity for discrete-time stochastic T-S fuzzy systems with time-varying delays is investigated. By constructing appropriate Lyapunov-Krasovskii functionals and employing stochastic analysis method and matrix inequality technique, a delay-dependent criterion to ensure the passivity for the considered T-S fuzzy systems is established in terms of linear matrix inequalities (LMIs) that can be easily checked by using the standard numerical software. An example is given to show the effectiveness of the obtained result.

Fuzzy control offers an alternative control approach for certain nonlinear systems [

On the other hand, the passivity theory is another effective tool for the stability analysis of system. The reason is mainly twofold:

Recently, some authors have studied the passivity of some systems and obtained sufficient conditions for checking the passivity of the systems that include linear systems with delays [

In this section, we consider a discrete-time T-S fuzzy system with stochastic disturbances and time-varying delay with the

Let

In the literature, different definitions of passivity have been used. Taking into account the stochastic nature of the T-S fuzzy systems considered in this paper, we adopt the definition in [

System (

Throughout this paper, we make the following assumption.

There exist matrices

In obtaining the main result of this paper, the following lemma will be useful for the proof.

Suppose that matrices

In this section, we will establish our main criterion based on the LMI approach. For presentation convenience, in the following, we denote that

Under Assumption

Defining

Calculating the difference of

From the definition of

When

From the first inequality of condition (

Denote that

When

In [

Consider a T-S fuzzy system (

By using the Matlab LMI Control Toolbox, we can find a solution to the LMIs in (

In this paper, the passivity for discrete-time stochastic T-S fuzzy systems with time-varying delays has been investigated. By constructing appropriate Lyapunov-Krasovskii functionals and employing stochastic analysis method and matrix inequality technique, a delay-dependent criterion to ensure the passivity for the considered T-S fuzzy systems has been established in terms of linear matrix inequalities (LMIs) that can be easily checked by using the standard numerical software. An example is also given to show the effectiveness of the obtained result.

The authors declare that there is no conflict of interests regarding the publication of this paper.

The authors would like to thank the editor and the reviewers for their valuable suggestions and comments which have led to a much improved paper. This work was supported by the National Natural Science Foundation of China under Grants 61273021 and 11172247 and in part by the Natural Science Foundation Project of CQ cstc2013jjB40008.