Stability analysis of delayed Takagi-Sugeno fuzzy systems via a membership-dependent reciprocally convex inequality. (English) Zbl 1539.93141
Summary: This article investigates the stability analysis of delayed Takagi-Sugeno (T-S) fuzzy systems. To begin with, a membership-dependent reciprocally convex inequality is proposed. Different from the frequently employed reciprocally convex inequalities, the proposed inequality can introduce the membership functions and provide a smaller bounding gap. Then, a suitable Lyapunov-Krasovskii functional (LKF) combined with the delay-product-type technique is established. As a consequence, two enhanced stability criteria for the delayed T-S fuzzy systems are developed. Lastly, the benefits of membership-dependent inequality are demonstrated by utilizing two well-known examples.
MSC:
| 93D05 | Lyapunov and other classical stabilities (Lagrange, Poisson, \(L^p, l^p\), etc.) in control theory |
| 93C42 | Fuzzy control/observation systems |
| 93C43 | Delay control/observation systems |
Keywords:
time-varying delay; stability; membership-function; fuzzy system; reciprocally convex inequalityReferences:
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