Abstract: This note is concerned with the switched systems consisting of single input-single output linear subsystems. The problem is to construct output feedback control analytically and make the closed-loop subsystems share a common quadratic Lyapunov function. Based on solvable Lie algebra condition and the complete form of the solution to generalized Sylvester equation, the eigenstructure assignment approach is proposed to establish the existent criterion of feedback control, through which the controller is explicitly formulated. A numerical example is worked out in detail to demonstrate the proposed method.