Further improvement of periodic control approach for relaxed stabilization condition of discrete-time Takagi–Sugeno fuzzy systems

In this paper, we present a new stabilization condition for discrete-time Takagi–Sugeno (T–S) fuzzy systems. To this end, the previously developed periodic nonparallel distributed compensation (non-PDC) control law is extended to the more general one whose gain matrix has a block lower triangular matrix form. A distinguished feature of the proposed control law is that it uses a discrete-time feedback loop incorporating information from the previous states of the system. The resultant stabilization condition is represented in the form of linear matrix inequalities (LMIs). In addition, we show that the proposed condition includes the existing one based on the periodic control approach as a particular case. Finally, examples are given to show that the proposed condition provides less conservative results than those of the existing ones published in the literature.