In this paper, a class of specified nonlinear systems are concerned. The nonlinear process model can be considered as a simplified Kolmogorov-Gabor polynomial model, which is motivated by considering the actuator nonlinearity and the process output nonlinearity. In terms of this nonlinear system, the analytical performance benchmark and the associated benchmark controller are established by minimizing the variance of the measurement output. The existence conditions of feedback invariant are discussed. The calculation of performance index, based on correlation analysis, is proposed. To facilitate assessment, a filtering or whitening method is presented. The white noise sequence is estimated by dynamic principal component analysis (DPCA), based on the nonlinear autoregressive exogenous (NARX) model. The numerical examples are given to illustrate the effectiveness of the proposed assessment method.