The state space average model of switching converters transforms time varying differential equations into time invariant differential equations by the averaging method in math. The model has merits of simple

clear physical conception and easy to design control system

but it exhibits significant steady-state error and delayed dynamic response in some special parameters or state conditions. Besides

the conventional state space average model (CSSAM) can't reflect how much the switching period influences system performance. The averaging method based on exact time domain solution approximation for the state variable is established in this paper. Subsequently

a second-order state-space average model (SOSSAM) which extends the constant term in CSSAM to a combination of constant term and linear term of the switching period is proposed. This model inherits the advantages of CSSAM and improves accuracy of steady state performance and dynamic response of switching converters. Influence of switching period to system performance is reflected

which lays a foundation for analyzing system performance and designing a control system of switching converters.