We consider the analytical controller design for a class of switched linear systems. Under suitable system assumptions, we propose a method using eigenstructure assignment that guarantees the closed-loop switched system is globally asymptotically stable under arbitrary switching signals, and the outputs achieve monotonic step reference tracking from all initial conditions. Additionally, the output signals from both subsystems can be made identical, so the effects of the system switching are not noticeable from the output. A constructive algorithm is provided that yields suitable feedback matrices, and the method is illustrated with a numerical example.