\(H_{\infty}\) stabilization criterion with less complexity for nonuniform sampling fuzzy systems. (English) Zbl 1284.93192
Summary: This paper investigates the problem of \(H_{\infty}\) stabilization for nonuniform sampling fuzzy systems. A method to design a fuzzy controller is proposed by taking the variation ranges of membership functions within sampling intervals into consideration. To reduce the computational complexity, Jensen’s integral inequality method is employed. Based on a well-known inequality, a convex combination technique is developed to deal with nonlinear time-varying coefficients derived from Jensen’s integral inequality. Combining with capturing the characteristic of sampled-data systems with a novel piecewise Lyapunov-Krasovskii functional (LKF), a less complex and less conservative \(H_{\infty}\) stabilization criterion is formulated as linear matrix inequalities (LMIs), which can be easily checked by using standard numerical software. Some illustrative examples are given to show the effectiveness of the proposed method and the significant improvement on the existing results.
MSC:
| 93D15 | Stabilization of systems by feedback |
| 93B36 | \(H^\infty\)-control |
| 93C42 | Fuzzy control/observation systems |
| 93C57 | Sampled-data control/observation systems |
Keywords:
sampled-data control; Takagi-Sugeno (T-S) fuzzy systems; fuzzy control; input delay approach; Jensen’s integral inequality method; linear matrix inequalities (LMIs)References:
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