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Relaxed delay-dependent stabilization criteria for discrete-time fuzzy systems based on a switching fuzzy model and piecewise Lyapunov functions
Received:March 16,2008  Revised:November 11,2008
Keywords:Delay-dependent  Fuzzy systems  Linear matrix inequalities (LMIs)  Piecewise Lyapunov function
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Zhile XIA, Junmin LI School of Science, Xidian University, Xian Shaanxi 710071, China; School of Mathematics and Information Engineering, Taizhou University, Taizhou Zhejiang 317000, China 
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Abstract:
      This paper presents delay-dependent stability analysis and controller synthesis methods for discrete-time Takagi-Sugeno (T-S) fuzzy systems with time delays. The T-S fuzzy system is transformed to an equivalent switching fuzzy system. Consequently, the delay-dependent stabilization criteria are derived for the switching fuzzy system based on the piecewise Lyapunov function. The proposed conditions are given in terms of linear matrix inequalities (LMIs). The interactions among the fuzzy subsystems are considered in each subregion, and accordingly the proposed conditions are less conservative than the previous results. Since only a set of LMIs is involved, the controller design is quite simple and numerically tractable. Finally, a design example is given to show the validity of the proposed method.
Zhile XIA, Junmin LI.Relaxed delay-dependent stabilization criteria for discrete-time fuzzy systems based on a switching fuzzy model and piecewise Lyapunov functions[J].Journal of Control Theory and Applications,2009,7(4):405~410.
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