<abstract xml:lang="en" xmlns="http://www.w3.org/1999/xhtml">This paper is concerned with the problem of stochastic stability and generalized <italic>H</italic>2 control for discrete-time fuzzy large-scale 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 <italic>H</italic>2 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.</abstract>

This paper is concerned with the problem of stochastic stability and generalized H2 control for discrete-time fuzzy large-scale 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.

Delay-dependent generalized <italic>H</italic>2 control for discrete T-S fuzzy large-scale stochastic systems with mixed delays

School of Science, Xidian University, South Taibai Rd 2, Xi'an, 710071, PR China

College of Mathematics and Computer Science, Yanan University, Yangjialing, Yan'an, 716000, PR China

School of Mathematics and Information Engineering, Taizhou University, Shifu Rd 1139, Taizhou, 317000, PR China

International Journal of Applied Mathematics and Computer Science

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

This paper is concerned with the problem of stochastic stability and generalized H2 control for discrete-time fuzzy large-scale stochastic systems with...

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

Published Online: Dec 21, 2011

Page range: 585 - 603

DOI: https://doi.org/10.2478/v10006-011-0046-6

Keywords
fuzzy large-scale stochastic system, delay-dependent, generalized control, infinite-distributed delays, linear matrix inequality

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