Design of a Polynomial Fuzzy Observer Controller With Sampled-Output Measurements for Nonlinear Systems Considering Unmeasurable Premise Variables

In this paper, we propose a polynomial fuzzy observer controller for nonlinear systems, where the design is achieved through the stability analysis of polynomial-fuzzy-model-based (PFMB) observer-control system. The polynomial fuzzy observer estimates the system states using estimated premise variables. The estimated states are then employed by the polynomial fuzzy controller for the feedback control of nonlinear systems represented by the polynomial fuzzy model. The system stability of the PFMB observer-control system is analyzed based on the Lyapunov stability theory. Although using estimated premise variables in polynomial fuzzy observer can handle a wider class of nonlinear systems, it leads to a significant drawback that the stability conditions obtained are nonconvex. Matrix decoupling technique is employed to achieve convex stability conditions in the form of sum of squares. We further extend the design and analysis to polynomial fuzzy observer controller using a sampled-data technique for nonlinear systems, where only sampled-output measurements are available. Simulation examples are presented to demonstrate the feasibility and validity of the design and analysis results.