Finite structure of LTV systems modelled by bond graph : an algebraic approach

Abstract

In this paper, the study of the finite structure of linear time varying systems modelled by bond graph is proposed with different approaches. Since from the bond graph model, different kind of mathematical relations can be directly derived, such as the state space representation, input-output relations or algebraic relations between variables defined either in a vector space or in a module (algebraic approach), different theoretical concepts can be used together in order to point out the finite structure of the model. In case of LTV models, mathematical calculus are not easily implemented because of the non commutativity between operations, thus a graphical methodology is pointed out directly on the bond graph representation. Even if finite zeros cannot be derived in each case, mathematical relations between variables which are related to the torsion module associated to the zeros are pointed out.