Model reference output feedback tracking for nonlinear systems via LMIs

This work addresses the tracking problem for nonlinear systems with unmeasured variables. We offer a new design methodology that is composed of a two-degrees-of-freedom scheme. The reference model must track a time-varying signal, and the controller employed can be regarded as one-degree-of-freedom. Then, based on the error between the outputs of the reference model and the plant, another controller is designed to ensure that this mismatch converges to zero. The reference model and the system are described as Takagi–Sugeno (TS) fuzzy models with nonlinear consequents (N-TS), which allows for separating measured from unmeasured variables. An advantage of the proposed scheme is that the controller for the reference model can be carried out using several methodologies from the literature, whereas the controller that governs the output error can be static or dynamic, whose design is based on Linear Matrix Inequalities (LMIs). Two examples are used to illustrate the validity of the developed control methodology and to compare it to another recent approach in the literature.