Relaxed observer design of discrete-time T-S fuzzy systems via a novel slack variable approach

•A novel slack variable approach is proposed.•The criterion takes the form of an LMI which is computationally tractable.•The obtained observer design conditions are less conservative.

The problem of further studies on observer design for discrete-time Takagi-Sugeno fuzzy systems is investigated in this paper. Different from the existing result, a new slack variable approach is presented by developing some useful matrix equalities which rely on both the current-time and the past-time normalized fuzzy weighting functions. As a result, the relaxation quality of recent fuzzy observer design is significantly enhanced. Moreover, the conditions for the existence of a fuzzy H∞ observer that minimizes an upper bound to H∞ norms are also proposed. Finally, two numerical examples are provided to show that the given results are less conservative than other results available in the literature.