In this paper, we propose to study the inversion of multivariable linear time varying systems modelled by bond-graph approach. Thus, an analysis method based on non-commutative differential algebra concepts is presented. The inverse and the reduced inverse models are studied in function of the decouplability of multivariable LTV system. To show the interest of this new method, several applications have been realized, among which is the thyristor circuit model TCSC often used in power electronics. This method can be implemented in software such as 20-sim or Symbol, in order to control the LTV systems in real time.