The authors consider the multidimensional stochastic differential system \[ \begin{aligned} dx_t&=[F_0(x_t)+F_1(x_t)u_t+\Delta F(t,x_t)] dt+\Theta_{1,t} dW_t,\\ dy_t&=C dx_t+\Theta_{2,t} dW_t,\\ d\widehat x_t&=(I+KC)^{-1}\big([F_0(\widehat x_t) +F_1(\widehat x_t)u_t] dt+K dy_t\big),\end{aligned} \] where \(x_t\) is the state (or signal) process, \(y_t\) is the output (or observable) process, \(u_t=u(t,\widehat x_t)\) is the input (or feedback control) process, and \(\widehat x_t\) is the high-gain observer. The main result of the paper is the derivation of the upper bound \(S^+\) for the observer performance index \[ {\mathcal L}_t :={1\over t}\int_0^t \big( \|\widehat x_\tau-x_\tau\|^2_1+\|\widehat x_\tau\|^2_2 \big) d\tau, \] where the norms \(\|\cdot\|_1\) and \(\|\cdot\|_2\) are defined by some positive matrices. It is shown that \(S^+\) is a linear combination of all a priori given uncertainty levels and that it is reachable. The proposed scheme is applied to a robot manipulator with unknown friction and inaccessible angular velocities.