For the stabilization problem of T-S fuzzy system, a new observer-based controller design approachis proposed when premise variables are not accessible. With a fuzzy observer, the estimated states error system isdescribed as two parts: unknown premise variable caused terms and observer error terms. Consider the property thatthe 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, aseries of linear matrix inequality conditions are proposed to asymptotically stabilize the system, the observer gainmatrices are used to overcome the uncertainties caused by UPVs. Finally a simulation example is used to illustratethe effectiveness of the proposed method, comparisons with traditional method shows the conservatism reductioneffects.
For the stabilization problem of T-S fuzzy system, a new observer-based controller design approachis proposed when premise variables are not accessible. With a fuzzy observer, the estimated states error system isdescribed as two parts: unknown premise variable caused terms and observer error terms. Consider the property thatthe 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, aseries of linear matrix inequality conditions are proposed to asymptotically stabilize the system, the observer gainmatrices are used to overcome the uncertainties caused by UPVs. Finally a simulation example is used to illustratethe effectiveness of the proposed method, comparisons with traditional method shows the conservatism reductioneffects.