A New Design of Fuzzy Affine Model-Based Output Feedback Control for Discrete-Time Nonlinear Systems

The observer-based output feedback control problem for nonlinear systems is studied through Takagi–Sugeno fuzzy affine models. A novel piecewise fuzzy affine observer is designed to estimate the unmeasurable state variables. To remove the assumptions in the existing works that the system input matrices and/or output matrices should be common, full rank, and uncertainties-free, a new approach is developed for the observer-based piecewise output feedback controller synthesis by making sufficient use of Young's inequality with its variance. Through fuzzy piecewise quadratic Lyapunov functions, improved and less conservative results on the output feedback controller design are obtained in terms of linear matrix inequalities, and the restrictions imposed in the existing results can be relaxed. Simulation studies are provided to confirm the effectiveness and conservatism reduction of the developed method.