LMI Robust Fuzzy C-Means Control for Nonlinear Systems

This paper addressed the robust fuzzy C-Means design for a class of clustering algorithm that are robust against both the plant parameter perturbations with nonlinearity and controller gain variations. Based on the description of Takagi–Sugeno (TS) fuzzy model, the stability and control of nonlinear systems are studied. The recently proposed integral inequality is selected based on the free weight matrix, and the minimum conservative stability criterion is given in the form of linear matrix inequality (LMI). Assuming that the controller and the system have the same premise, this method does not require the number and membership function rules. In addition, the improved control is used as the stability criterion of the closed-loop TS fuzzy system obtained from LMI in large-scale nonlinear systems, and is reorganized for machine learning. The novelty of this paper is to develop a simplified and robust controller design for a class of nonlinear perturbed systems. Moreover, the proposed control process was also ensured by the control criterion derived from the energy function for the stability of the nonlinear system. Finally, a simulation is given and demonstrated the feasibility of the practical application motivated by certain concrete-real problem in vibrated structures.