Robust stabilization design of nonlinear stochastic partial differential systems: Fuzzy approach

Abstract

In this paper, we address the robust stabilization design problem for nonlinear stochastic partial differential systems (NSPDSs) in the presence of random external disturbances and measurement noise in the spatio-temporal domain. We propose a fuzzy stochastic partial differential system to approximate the NSPDSs based on fuzzy interpolation approach. Next, we develop a fuzzy stochastic spatial state space model to represent the fuzzy stochastic partial differential system by employing a semi-discretization finite difference scheme. Based on this model, we propose a robust fuzzy estimator-based stabilization controller to stabilize the NSPDSs. Furthermore, robust stochastic H∞ stabilization design is suggested to attenuate the effects of random external disturbances and measurement noise in the spatio-temporal domain from the area energy point of view. The LMI technique is applied to solve the issue of control gains and estimator gains of the controller by using a systematic control design procedure. Finally, a simulation is presented as an example to illustrate the design procedure and to confirm the performance of the proposed robust fuzzy estimator-based stabilization design for the NSPDSs.