Sampled-Data Fuzzy Stabilization of Nonlinear Systems Under Nonuniform Sampling

This paper investigates the sampled-data fuzzy stabilization problem for a class of nonlinear systems that is exactly modeled in Takagi-Sugeno fuzzy form at least locally. A new method for designing parallel distribution compensation fuzzy controller is proposed, which just requires that the nonlinear function is locally Lipschitz. By considering the sample-and-hold behavior of the system and using Jensen's integral inequality, an inequality constrain condition is derived from the locally Lipschitz property. Further, by defining a time-dependent Lyapunov-Krasovskii functional term, a new technique instead of the use of S-procedure is developed, and stabilization conditions for state feedback and observer-based output feedback under nonuniform sampling are obtained. Compared with the existing ones, the new design method not only avoids the difficulty of finding exact upper bounds of asynchronous errors of mismatch membership functions, but contains less conservatism and less numerical complexity as well. Finally, some illustrative examples are given to show the effectiveness of the proposed design method and the significant improvement over the existing results.