Stability and controller design for T-S fuzzy discrete-time systems with time-varying delay in the state

We propose delay dependent convex conditions for stability analysis and synthesis of stabilizing fuzzy state feedback controllers for Takagi-Sugeno (T-S) fuzzy discrete-time systems with time-varying delay in the state. The delay is considered limited by upper and lower values. The proposed conditions are formulated in terms of linear matrix inequalities (LMIs) yielding efficient numerical behavior. Additionally, the design control law dismiss the real time knowledge of the delay, simplifying the controller implementation. Moreover, the proposed synthesis conditions can lead to less conservative design as it is illustrate by means of three numerical examples. Some recent conditions found in the literature are used to establish a numerical comparison with our approach.