Fuzzy rule-based combination of linear and switching state-feedback controllers

This paper presents a fuzzy rule-base combined controller, which is a fuzzy rule-based combination of linear and switching state-feedback controllers, for nonlinear systems subject to parameter uncertainties. The switching state-feedback controller is employed to drive the system states toward the origin. When the system state approaches the origin, the linear state-feedback controller will gradually replace the switching state-feedback controller. The smooth transition between the linear and switching state-feedback controllers is governed by the fuzzy rules. By using the fuzzy rule-based combination technique, the proposed fuzzy rule-base combined controller integrates the advantages of both the linear and switching state-feedback controllers but eliminates their disadvantages. As a result, the proposed fuzzy controller provides good performance during the transient period and the chattering effect is removed when the system state approaches the origin. Stability conditions will be derived to guarantee the system stability. Furthermore, a saturation function is employed to replace the switching component to alleviate the chattering during the transient period. By using the proposed fuzzy rule-based combination technique, the steady state error introduced by the saturation function can be eliminated. Application examples will be given to show the merits of the proposed approach.