Sampled-data observer-based output-feedback fuzzy stabilization of nonlinear systems: Exact discrete-time design approach

This paper presents a new direct discrete-time design methodology of a sampled-data observer-based output-feedback fuzzy controller for a class of nonlinear system that is exactly modeled in Takagi–Sugeno's form at least locally. A fundamental yet challenging issue in this direction is the unavailability of the exact discrete-time model of the nonlinear plant in a closed form. In contrast to the earlier works that are based on an approximate discrete-time model thus the stability obtained in the design step is not preserved in the implementation step, we employ an exact discrete-time fuzzy model in an integral form. Sufficient asymptotic stabilization conditions are investigated in the discrete-time Lyapunov sense. We then show that the resulting sampled-data controller indeed asymptotically stabilizes the nonlinear plant. An example is provided to illustrate the effectiveness of the proposed methodology.