Output feedback fuzzy controller design with local nonlinear feedback laws for discrete-time nonlinear systems

Abstract—This paper considers the output feedback control problem for nonlinear discrete-time systems, which are repre-sented by a type of fuzzy systems with local nonlinear models. By using the estimations of the states and nonlinear functions in local models, sufficient conditions for designing observer-based controllers are given for discrete-time nonlinear systems. First, a separation property, i.e., the controller and the observer can be independently designed, is proved for the class of fuzzy sys-tems. Second, a two-step procedure with cone complementarity linearization algorithms is also developed for solving the H∞ dynamic output feedback (DOF) control problem. Moreover, for the case where the nonlinear functions in local submodels are measurable, a convex condition for designing H ∞ controllers is given by a new DOF control scheme. In contrast to the existing methods, the new methods can design output feedback controllers with fewer fuzzy rules as well as less computational burden, which is helpful for controller designs and implementations. Lastly, nu-merical examples are given to illustrate the effectiveness of the proposed methods. Index Terms—Cone complementarity linearization (CCL),H∞ control, linear matrix inequality (LMI), nonlinear discrete-time systems, separation property, state observer. I