To overcome the issues of severe cross-influence and slow transient response at the output end of the traditional common-mode-differential-mode controlled single-inductor dual-output (SIDO) converter, a switching control strategy based on a common Lyapunov function is proposed. First, according to the theory of switched systems, all subsystems of the SIDO Buck converter are analyzed and a switching affine system model of the SIDO Buck converter is established. Second, the solution of the common Lyapunov function is transformed into the solution of a linear matrix expression and the switching control law is designed according to the positive-definite matrix P of the linear matrix inequality. Finally, the proposed control strategy is verified by simulation in PSIM. The results show that the proposed control strategy has faster response speed and anti-interference ability and effectively reduces cross-influence.