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The paper addresses a systematic procedure to deal with state and parameter uncertainty estimation for nonlinear time-varying systems. A robust observer with respect to states, inputs and perturbations is designed, using a Takagi–Sugeno (T–S) approach with unknown premise variables. Tools of the linear automatic to the nonlinear systems are applied, using the Linear Matrix Inequalities optimization. The observer estimates the uncertainties, the states and minimizes the effect of external disturbances on the estimation error. The uncertainties are modelled in a polynomial way which allows considering the 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. The method performance is illustrated using the three-tank system. [ABSTRACT FROM AUTHOR]

Interval analyses are well known in the mathematics literature but have found few applications in control engineering. Based on the interval concept, we present here a methodology for data reconciliation and mass balance equilibration which is a very classical problem in mineral and chemical engineering. Indeed, this problem is solved with the view of inequality constraints which allows us to represent measurements by interval without particular knowledge and hypothesis about the density probability function of the measurement errors. As a main result, the paper gives a set of solutions for the reconciled data under an interval form and not only one solution as is the case with classical approaches. [ABSTRACT FROM AUTHOR]