The aim of this paper is to expose a fashion to introduce transient stability constraints into the problem of stabilizers coordination solved by an optimal criterion. The problem is posed in such a way that different operating conditions and fault locations may be taken into account, leading to robust stabilizers. The proposed procedure is based on minimizing the incremental real part of modes of concern; such increments are evaluated through second order sensitivities. Inequality constraints are embedded into the problem in order to circumscribe the angular excursions by the stabilizers' action. A nine-bus power system is considered as a sample system to exhibit the main results of the proposed methodology.