Unknown input based observer synthesis for uncertain Takagi–Sugeno fuzzy systems

Observer design for a Takagi–Sugeno (T–S) fuzzy system with uncertainties is extremely difficult because the estimation error is incapable of approaching zero asymptotically due to the existence of uncertainty terms. In this study, by regarding the uncertainty as an unknown input, with some particular derivation, the authors successfully synthesize a fuzzy observer which guarantees that the error will converge to zero asymptotically. Based on Lyapunov theory and linear matrix inequality tools, the main theorem is derived for the fuzzy observer synthesis. This study does not limit the size of uncertainties, but the uncertainties have to satisfy a specific matching condition in order to use the unknown input concept. Finally, a numerical example is given to show that the proposed approach is effective in estimating system's states subject to system uncertainties.