Abstract: The problem of stabilization of third-order switched systems is considered. A new sufficient condition is presented for the third-order linear control system to share a positive definite matrix as a quadratic Lyapunov function. Then, it is proved that the third-order switched systems are quadratically stabilizable under appropriate conditions. The control laws, which stabilize the switched systems, are designed, and a straightforward computation algorithm for solving the quadratic stabilization problem is presented.