In this research, we apply the observer approach introduced by Djennoune et al.  [1] to estimate water levels in a coupled tanks system. Central to this approach is the use of a remarkable modulating function-based transformation \(T_n \) , which employs a time/output-dependent coordinate transformation. This transformation converts the original system into a form where the effects of initial conditions are effectively nullified. The primary advantage of utilizing the \(T_n\) transformation is its ability to achieve instantaneous convergence, ensuring both rapid and accurate state estimation. The observer’s finite-time convergence is assured, with the estimation error remaining bounded within a finite period. Numerical simulations further validate the effectiveness of this method for the coupled tanks system, demonstrating the robustness of the \(T_n \) transformation in practical applications. A comparison with the sliding mode observer highlights its superior performance in reducing the peaking phenomenon.