Fuzzy sliding mode controller design for uncertain time-delayed systems with nonlinear input. (Q1414812)

An uncertain time-delayed linear dynamical system with a nonlinear input is considered. First, a variable structure control is used to drive the trajectories of the system into the sliding mode. Next, a fuzzy sliding mode control is proposed. The main idea is to use the reaching condition \(s \dot s <0\), and let \(s\) and \(\dot s\) be fuzzy variables. The rule table is then constructed in a two-dimensional space (for example, if \(s\) and \(\dot s\) have seven membership functions respectively, then the fuzzy rules will have forty nine rules). A simulation example illustrates the features of the proposed fuzzy controller.