Robust observer-based controller design for Takagi–Sugeno systems with nonlinear consequent parts

This paper considers the design of robust observer-based controller for a class of continuous-time nonlinear systems with disturbances. The system is presented by Takagi–Sugeno (TS) model with nonlinear consequents. The proposed TS structure reduces the number of rules in the Sugeno model by using local nonlinear rules. It is assumed that the nonlinearities satisfy a sector condition as well as an incremental quadratic constraint. These constraints are fuzzified to reduce the conservativeness. The proposed controller guarantees H∞H∞ performance of the system by using Linear Matrix Inequality (LMI) formulation. Moreover, the proposed observer benefits from a nonlinear injection term to add more degrees of freedom to the LMIs. Numerical examples illustrate effectiveness of the proposed method as compared to the existing methods in literature in terms of performance and enlarging the class of system.