Fuzzy-based output-feedback H1 control for uncertain nonlinear systems: an LMI approach

The problem of robustly stabilising a class of nonlinear systems using an H1 fuzzy observer-based controller is considered. A class of nonlinear systems is approximated by a Takagi–Sugeno fuzzy model. A sufficient condition is derived to ensure the robust stability of the fuzzy observer-based controller with guaranteed H1 disturbance attenuation level. The observer and controller design problem is cast in the form of bilinear matrix inequalities (BMIs). Using a two-step procedure, these BMIs are reduced to two sets of linear matrix inequalities that can be solved very efficiently using convex optimisation techniques. The proposed design procedure extends previous results by considering both the premise uncertainty and the consequent uncertainty simultaneously. Furthermore, a modified two-step procedure is suggested for plants with linear output equation. Finally, a simulation example illustrates the validity and applicability of the given approach.