State, unknown input and uncertainty estimation for nonlinear systems using a Takagi-Sugeno model

The paper addresses a systematic procedure to deal with the state, unknown input and parameter uncertainty estimation for nonlinear time-varying systems. This is realized by designing a robust observer for dynamic nonlinear systems using a Takagi-Sugeno (T-S) multi-model (MM) approach with nonlinear outputs. The method applies the technique of descriptor systems by considering unknown inputs and parameter uncertainty as auxiliary state variables. This approach allows to apply the tools of the linear automatic to dynamic nonlinear systems by using the Linear Matrix Inequalities (LMI) optimization. The observer estimates the previous mentioned variables and minimizes the effect of external disturbances on the estimation error. The model uncertainties are included in the model in a polynomial way which allows to consider the model uncertainty estimation as a fault detection problem. The residual sensitivity to faults while maintaining robustness according to a noise signal is handled by ℋ_∞/ℋ_- approach.