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.