Linear time varying systems stability with linearly dependent state variables in the physical domain

A bond graph model of a Linear Time-Varying (LTV) system is proposed. This bond graph can contain LTV constitutive relations of the fields, and transformer and gyrator LTV modules. Also, the bond graph model can have storage elements in integral and derivative causality assignments, i.e. the state variables can be linearly independent or linearly dependent. Then, the corresponding junction structure and the state variables representation of the bond graph can be obtained. Thus, a Lemma to get the stability conditions of a LTV system by using the junction structure of the bond graph is presented. The proposed methodology to determine the stability conditions is applied to two examples.