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Observer-based Controller Design for A T-S Fuzzy System with Unknown Premise Variables

Wen-Bo Xie*, He Li, Zhen-Hua Wang, and Jian Zhang
International Journal of Control, Automation, and Systems, vol. 17, no. 4, pp.907-915, 2019

Abstract : "For the stabilization problem of T-S fuzzy system, a new observer-based controller design approach is proposed when premise variables are not accessible. With a fuzzy observer, the estimated states error system is described as two parts: unknown premise variable caused terms and observer error terms. Consider the property that the norm of the unknown premise variable caused terms are under a Lipschitz condition constraint of observer error, an observer and controller errors augmented system is obtained. Then based on the Lyapunov function method, a series of linear matrix inequality conditions are proposed to asymptotically stabilize the system, the observer gain matrices are used to overcome the uncertainties caused by UPVs. Finally a simulation example is used to illustrate the effectiveness of the proposed method, comparisons with traditional method shows the conservatism reduction effects."

Keyword : Controller, observer, T-S fuzzy system, unknown premise variables.

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