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

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.