This paper is devoted to constructive approximations and an alternative theoretic characterization of some classes of sliding mode control processes. We construct the consistent approximations of the differential inclusions associated with the 1rst order variable structures dynamics and also propose a variational description of the sliding mode control in the framework of an auxiliary Hamiltonian based formalism. A trajectory of the closed-loop systems can be then constructively specifed as a result of a particular system optimization procedure applied to the original model. The presented approximations and variational description of the sliding mode-type control design can provide a new analytic basis for constructive numerical schemes and implementable control algorithms. The mathematical tool elaborated in our contribution constitutes a formal extension of the classic Fillipovs results.