We are considering the control design problem for switched linear systems. We propose a method for the design of state-feedback controllers for the individual subsystems such that the closed-loop systems share a common eigenstructure. If additionally the eigenvalues of each individual subsystem can be chosen stable then the resulting switched system is stable for arbitrary switching. We present a necessary and a sufficient condition for which such controllers exist for systems of arbitrary order. For third-order systems, we show that a common eigenstructure can always be obtained by state-feedback given that the number of inputs offer enough degrees of freedom. We present a constructive procedure to obtain feedback controls such that the closed-loop systems have common eigenstructures. In all but one degenerated case the eigenvalues can be chosen arbitrarily such that the resulting closed-loop switched system is rendered asymptotically stable for arbitrary switching. We present an example for the degenerated case, where the eigenstructure may only be rectified if one of the closed-loop systems has a positive eigenvalue.