Robust output feedback controller design of discrete-time Takagi–Sugeno fuzzy systems: a non-monotonic Lyapunov approach

This study proposes a robust dynamic output feedback controller design for a class of discrete-time non-linear systems described by Takagi–Sugeno (T–S) fuzzy models using a non-monotonic Lyapunov approach. In the non-monotonic Lyapunov approach, the monotonicity requirement of the standard Lyapunov approach is not required. Based on the non-monotonic Lyapunov approach, sufficient conditions for the existence of an output stabilising feedback controller for discrete T–S fuzzy systems with and without uncertainties are derived in terms of linear matrix inequalities. The proposed design significantly reduces the conservativeness of the existing output feedback controller designs. An numerical example is used to illustrate the effectiveness of the proposed design.