Stability and stabilization for delayed fuzzy systems via reciprocally convex matrix inequality. (English) Zbl 1464.93039
Summary: This paper focuses on the problems of stability and stabilization for time-delayed fuzzy systems. By establishing a novel Lyapunov-Krasovskii functional (LKF) and using an extended reciprocally convex matrix inequality with auxiliary function integral inequality, an improved stability condition is proposed. To further improve the results, a delay-product-type term is introduced into the LKF. Then, a delay-dependent stabilization condition is developed based on parallel distributed compensation (PDC) scheme by some linearization techniques. Finally, the efficiency and benefits of the stability criterion and controller design method are illustrated by several classical numerical examples.
MSC:
| 93C42 | Fuzzy control/observation systems |
| 93D20 | Asymptotic stability in control theory |
| 93D15 | Stabilization of systems by feedback |
| 93C15 | Control/observation systems governed by ordinary differential equations |
| 34K20 | Stability theory of functional-differential equations |
| 34K36 | Fuzzy functional-differential equations |
| 93C43 | Delay control/observation systems |
Keywords:
T-S fuzzy systems; time-varying delay; stabilization; extended reciprocally convex matrix inequalityReferences:
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