Fuzzy Boundary Sampled-Data Control for Nonlinear DPSs With Random Time-Varying Delays

This article introduces a fuzzy boundary sampled-data (SD) control approach for a nonlinear distributed parameter system (DPS) with random time-varying delay, which belongs to two intervals and is considered by a probabilistic way to take the influence of uncertain factors, and boundary and distributed SD measurements are respected. Initially, this nonlinear DPS is represented precisely by a Takagi–Sugeno (T–S) fuzzy delayed partial differential equation (PDE) model. Subsequently, a fuzzy boundary SD control design is achieved under boundary and distributed SD measurements, employing linear matrix inequalities based on the T–S fuzzy delayed PDE model. This design ensures mean square exponential stability for the closed-loop delayed DPS through the use of inequality techniques and a Lyapunov functional. The membership functions of the proposed fuzzy boundary SD control law are independent of the fuzzy delayed PDE plant model and determined by the measurement output. Finally, the effectiveness of the designed fuzzy boundary SD controller is demonstrated via two simulation examples.