This paper is devoted to the Lyapunov - type stability analysis for a class of dynamic systems in the presence of a specific time - driven switchings mechanism. We consider dynamic stability problem for the whole set of implicit global representations associated with a class of linear switched systems. The resulting closed - loop dynamic model is determined by a PD - like state feedback control. For the corresponding systemanalysis associated with the resulting system we propose a common Lyapunov function that makes it possible to establish some basic stability properties. The obtained results have a constructive nature and can be applied to a wide class of switched systems.