PD Control-Based Reachable Set Synthesis for Singular Takagi–Sugeno Fuzzy Systems With Time-Varying Delay

This article focuses on the reachable set synthesis problem for singular Takagi–Sugeno fuzzy systems with time-varying delay. The main contribution is that we design a proportional plus derivative state feedback controller to ensure that the singular fuzzy system is normal and the system states are bounded by a derived ellipsoid. In the light of the Lyapunov stability theory and the parallel distributed compensation method, the sufficient criteria are shown in the format of linear matrix inequalities. Furthermore, we investigate another case of reachable set synthesis, where the reachable set to be found is contained in a given ellipsoid. Finally, we use two examples to exhibit the usefulness of the proposed method.