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Improved delay-dependent stability criteria for T-S fuzzy systems with time-varying delay. (English) Zbl 1334.93110
Summary: This paper is concerned with the robust stability of uncertain T-S fuzzy systems with time-varying delay. A novel Lyapunov-Krasovskii functional is established by employing the idea of combining delay-decomposition with state vector augmentation. Then, by employing some integral inequalities and the reciprocally convex approach, some less conservative delay-dependent stability criteria are obtained. The proposed stability conditions are formulated in the form of linear matrix inequalities (LMIs), which can be solved efficiently with Semi-Definite Programming (SDP) solvers. Finally, four numerical examples are provided to show that the proposed conditions are less conservative than existing ones.

MSC:
93C42 Fuzzy control/observation systems
34K20 Stability theory of functional-differential equations
34K36 Fuzzy functional-differential equations
93D05 Lyapunov and other classical stabilities (Lagrange, Poisson, \(L^p, l^p\), etc.) in control theory
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