A multiple Lyapunov function approach for robust H∞ observer-based tracking control of uncertain T-S fuzzy systems

In this paper, the problem of robust H_∞ fuzzy observer-based tracking control for the uncertain T-S fuzzy systems with external disturbances is addressed. The robust stability synthesis is based on the descriptor redundancy approach. Linear matrix inequalities (LMIs) are proposed for the design of the observer-based controller. Less conservative design conditions are obtained using a multiple Lyapunov function approach. It is assumed that the derivatives of the grades of the fuzzy membership functions exist and have lower bounds. This assumption is not restrictive in many T-S fuzzy models. Unlike the previous design method for robust H_∞ fuzzy observer-based tracking controller which needs four prescribed scalar variables, the proposed method in this paper gives strict linear matrix inequalities. Moreover, in order to cover a more general problem, it is assumed that there exist uncertainties in local system, input and output matrices simultaneously for the uncertain T-S fuzzy system. A numerical example is used to show the effectiveness of the proposed method.