Output tracking control for fuzzy systems via output feedback design

Fuzzy observer-based control design is proposed to deal with the output tracking problem for nonlinear systems. For the purpose of tracking design, the new concept of virtual desired variables and, in turn the so-called generalized kinematics are introduced to simplify the design procedure. In light of this concept, the design procedure is split into two steps: i) Determine the virtual desired variables from the generalized kinematics; and ii) Determine the control gains just like solving linear matrix inequalities for stabilization problem. For immeasurable state variables, output feedback design is proposed. Here, we focus on a common feature held by many physical systems where their membership functions of fuzzy sets satisfy a Lipschitz-like property. Based on this setting, control gains and observer gains can be designed separately. Moreover, zero tracking error and estimation error are concluded. Three different types of systems, including nonlinear mass-spring systems, dc-dc converters, and induction motors are considered to demonstrate the design procedure. Their satisfactory simulation results verify the proposed approach.