Rosenbrock models and their homotopy equivalence Original Research Article

As is known, the notion of homotopy equivalence is a fundamental notion of mathematics and was introduced in order to formalize a relation that is weaker than isomorphism. In this note we define a homotopy equivalence of Rosenbrock systems and show that it coincides with the classical equivalences of Rosenbrock and Fuhrmann. Next, we show that the homotopy equivalence does preserve the important properties of a system (including the properties at infinity when these are properly understood). Finally, we define in a simple manner the states and motions of a system and claim that they are homotopy invariants.