# Delay-dependent generalized H₂ control for discrete T-S fuzzy large-scale stochastic systems with mixed delays

Jiangrong Li; Junmin Li; Zhile Xia

International Journal of Applied Mathematics and Computer Science (2011)

- Volume: 21, Issue: 4, page 585-603
- ISSN: 1641-876X

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topJiangrong Li, Junmin Li, and Zhile Xia. "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 21.4 (2011): 585-603. <http://eudml.org/doc/208072>.

@article{JiangrongLi2011,

abstract = {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 (DDPLKF) 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.},

author = {Jiangrong Li, Junmin Li, Zhile Xia},

journal = {International Journal of Applied Mathematics and Computer Science},

keywords = {fuzzy large-scale stochastic system; delay-dependent; generalized H₂ control; infinite-distributed delays; linear matrix inequality; generalized $H_\{2\}$ control},

language = {eng},

number = {4},

pages = {585-603},

title = {Delay-dependent generalized H₂ control for discrete T-S fuzzy large-scale stochastic systems with mixed delays},

url = {http://eudml.org/doc/208072},

volume = {21},

year = {2011},

}

TY - JOUR

AU - Jiangrong Li

AU - Junmin Li

AU - Zhile Xia

TI - Delay-dependent generalized H₂ control for discrete T-S fuzzy large-scale stochastic systems with mixed delays

JO - International Journal of Applied Mathematics and Computer Science

PY - 2011

VL - 21

IS - 4

SP - 585

EP - 603

AB - 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 (DDPLKF) 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.

LA - eng

KW - fuzzy large-scale stochastic system; delay-dependent; generalized H₂ control; infinite-distributed delays; linear matrix inequality; generalized $H_{2}$ control

UR - http://eudml.org/doc/208072

ER -

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