Linear control system was originally studied in time domain, but it was very difficult to solve higher-order differential equations at that time. People use Laplace transform and Fourier transform as mathematical tools to transform differential equations into algebraic equations, and then analyze and design control systems in frequency domain. Frequency domain method is widely used in practice because of its clear physical meaning, simple calculation and robust controller design. G. Zames put forward the idea of H∞ control in 198 1. The main idea is to take the H∞ norm of the transfer function between some signals in the system as the optimization index. It is hoped that the frequency response of the interference spectrum to the output will be minimal for the following problems. Judging from the current research situation, H∞ control theory mainly discusses the solution method of H∞ in time domain, but the idea it reveals is a frequency domain synthesis method, which can be used to synthesize nonlinear control systems. Based on the description of generalized frequency response function, it is an important research direction to study the solution of H∞ control for nonlinear control systems in multidimensional frequency domain space.