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RESEARCH PRODUCT

Novel Stability Criteria for T--S Fuzzy Systems

Lixian ZhangPeng ShiHamid Reza KarimiXudong Zhao

subject

Lyapunov functionpolynomialsFuzzy setStability (learning theory)Lyapunov function; membership-dependent; stability; Takagi-Sugeno (T-S) fuzzy system; Control and Systems Engineering; Computational Theory and Mathematics; Artificial Intelligence; Applied Mathematicssymbols.namesakevectorsTakagi-Sugeno (T-S) fuzzy systemComputer Science::Systems and ControlArtificial IntelligenceControl theoryLyapunov equationLyapunov redesignLyapunov methodsMathematicsLyapunov functionDegree (graph theory)membership-dependentstability criteriaApplied Mathematicseducational institutionsFuzzy control systemstabilityStability conditionsComputational Theory and MathematicsControl and Systems Engineeringfuzzy systemssymbols

description

In this paper, novel stability conditions for Takagi-Sugeno (T-S) fuzzy systems are presented. The so-called nonquadratic membership-dependent Lyapunov function is first proposed, which is formulated in a higher order form of both the system states and the normalized membership functions than existing techniques in the literature. Then, new membership-dependent stability conditions are developed by the new Lyapunov function approach. It is shown that the conservativeness of the obtained criteria can be further reduced as the degree of the Lyapunov function increases. Two numerical examples are given to demonstrate the effectiveness and less conservativeness of the obtained theoretical results. Refereed/Peer-reviewed

yearjournalcountryeditionlanguage
2014-04-01IEEE Transactions on Fuzzy Systems
https://doi.org/10.1109/tfuzz.2013.2254491