H∞ Observer-Based Control for Uncertain Takagi-Sugeno Fuzzy Systems with Application to a four-Tank Process

The design of H-infinity observer-based controllers for nonlinear systems represented by Takagi-Sugeno models in continuous time is studied here, in the presence of parameter uncertainties and external disturbances. Conditions are developed in terms of Linear Matrix Inequalities (LMIs), thanks to a change of variables to avoid bilinear terms. Thanks to this, observer and controller gains can be deduced in terms of LMIs conditions, which can be practically solved in a single step. The simulation of a four-tank lab system is used to show the advantage of the methodology proposed, revealing a good compromise between the controller simplicity and conservatism, outperforming previous approaches.