The approach adopted in this paper for the problem of transient stabilization of multimachine power systems sees the entire network as the (structure-preserving) interconnection of the network components, described by well-known models. We first show that, under the assumptions of non-resistive loads and zero transfer conductances on the lines, these models admit a Hamiltonian description and are, then, shown to be cyclo-dissipative with storage functions akin to power. Our main contribution is the identification-in terms of Linear Matrix Inequality (LMI) -of a class of power systems with resistive loads and leaky lines for which we can design generator excitation controllers that (locally) stabilize the desired equilibrium point. Since the LMI depends explicity on the controller gain, a decentralized control action can be easily computed. The proposed technique is applied to a classical example. Keywords Power systems transient stability, energy shaping, dissipativity