Tensor systems are a framework for modeling of multilinear hybrid systems with discrete and continuous valued signals. Two examples from building services engineering and multi-agent systems show applications of this framework. A tensor model of a heating system is derived and approximated by tensor decomposition methods first. Second, a tensor model of a multi-agent system with a structure already given in a decomposed form is reduced further by the same decomposition methods. The validity of these low rank approximations is shown for both examples.