Geodesic
Delay-dependent generalized H2 control for discrete T-S fuzzy large-scale stochastic systems with mixed delays
International Journal of Applied Mathematics and Computer Science, Tome 21 (2011) no. 4, pp. 585-603.

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This paper is concerned with the problem of stochastic stability and generalized H2 control for discrete-time fuzzy largescale stochastic systems with time-varying and infinite-distributed delays. Large-scale interconnected systems consist of a number of discrete-time interconnected Takagi-Sugeno (T-S) subsystems. First, a novel Delay-Dependent Piecewise Lyapunov-Krasovskii Functional (DDPLKF0 is proposed, in which both the upper and the lower bound of delays are considered. Then, two improved delay-dependent stability conditions are established based on this DDPLKF in terms of Linear Matrix Inequalities (LMIs). The merit of the proposed conditions lies in its reduced conservatism, which is achieved by circumventing the utilization of some bounding inequalities for cross products of two vectors and by considering the interactions among the fuzzy subsystems in each subregion. A decentralized generalized H2 state feedback fuzzy controller is designed for each subsystem. It is shown that the mean-square stability for discrete T-S fuzzy large-scale stochastic systems can be established if a DDPLKF can be constructed and a decentralized controller can be obtained by solving a set of LMIs. Finally, an illustrative example is provided to demonstrate the effectiveness of the proposed method.
Keywords: fuzzy large scale stochastic system, delay-dependent, generalized H2 control, infinite distributed delays, linear matrix inequality
Mots-clés : system stochastyczny, opóźnienie zależne, liniowa nierówność macierzowa 
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Li, J.; Li, J.; Xia, Z. Delay-dependent generalized H2 control for discrete T-S fuzzy large-scale stochastic systems with mixed delays. International Journal of Applied Mathematics and Computer Science, Tome 21 (2011) no. 4, pp. 585-603. http://geodesic.mathdoc.fr/item/IJAMCS_2011_21_4_a0/

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