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Title: LMI-based stability and performance conditions for continuous-time nonlinear systems in Takagi-Sugeno's form
Authors: Lam, HK
Leung, FHF 
Issue Date: Oct-2007
Source: IEEE transactions on systems, man, and cybernetics. Part B, Cybernetics, Oct. 2007, v. 37, no. 5, p. 1396-1406
Abstract: This correspondence presents the stability analysis and performance design of the continuous-time fuzzy-model-based control systems. The idea of the nonparallel-distributed-compensation (non-PDC) control laws is extended to the continuous-time fuzzy-model-based control systems. A nonlinear controller with non-PDC control laws is proposed to stabilize the continuous-time nonlinear systems in Takagi-Sugeno's form. To produce the stability-analysis result, a parameter-dependent Lyapunov function (PDLF) is employed. However, two difficulties are usually encountered: 1) the time-derivative terms produced by the PDLF will complicate the stability analysis and 2) the stability conditions are not in the form of linear-matrix inequalities (LMIs) that aid the design of feedback gains. To tackle the first difficulty, the time-derivative terms are represented by some weighted-sum terms in some existing approaches, which will increase the number of stability conditions significantly. In view of the second difficulty, some positive-definitive terms are added in order to cast the stability conditions into LMIs. In this correspondence, the favorable properties of the membership functions and nonlinear control laws, which allow the introduction of some free matrices, are employed to alleviate the two difficulties while retaining the favorable properties of PDLF-based approach. LMI-based stability conditions are derived to ensure the system stability. Furthermore, based on a common scalar performance index, LMI-based performance conditions are derived to guarantee the system performance. Simulation examples are given to illustrate the effectiveness of the proposed approach.
Keywords: Fuzzy control
Parameter-dependent Lyapunov function (PDLF)
Performance realization
Stability analysis
Publisher: Institute of Electrical and Electronics Engineers
Journal: IEEE transactions on systems, man, and cybernetics. Part B, Cybernetics 
ISSN: 1083-4419
DOI: 10.1109/FUZZY.2006.1681980
Rights: © 2007 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE.
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