In order to establish the seismic design and a dynamic reliability analysis method of the damper protection system of general linear viscoelastic energy dissipation structure with braces，a general analytical solution of the response of the damper protection system of the general linear viscoelastic energy dissipation structure with braces under the non-uniform and completely nonstationary seismic excitation is proposed in this paper. The most general integral type analysis model with support viscoelastic damper is used to realize the non-extended order modeling of the general linear viscoelastic damping energy dissipation structure system with braces by using differential integral equations. The non-extended order mode superposition solution of the transient response of the damper protection system under arbitrary excitation and non-zero initial conditions is directly obtained by using the transfer matrix method. By using the analytical solution and the frequency domain analysis method of random vibration，the specific response analytical solutions of the damper protection system of energy dissipation structure are obtained under the general and eight classical uniform and non-uniform modulation filtered white noise seismic excitation and completely non-stationary seismic power spectrum models. The correctness，simplicity and universality of this method are proved by the theoretical verification analysis of the complex mode method and frequency response function method of two typical structures of vibration absorption and isolation，as well as the response analysis of uniform，non-uniform and completely non-stationary cases. The obtained analytical solutions of transient response and non-stationary seismic response can，on the one hand，carry out Poisson based analysis on the components of the overall energy dissipation system. On the other hand，it will provide an analysis path for the structural system to establish the mode superposition seismic design based on response spectrum.