The aim of this paper is to provide a robust observer design using a Linear Matrix Inequality (LMI) technique along with the analysis and comparison of the interval observer and set-membership approaches within the state estimation framework. The propagation of the uncertainty is taken into account considering a zonotopic-set representation. Both approaches are compared and related using Linear Quadratic Regulator (LQR). Finally, a simulation example based on a three-tank system is employed to both illustrate and discuss the effectiveness of the proposed approach.

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