On higher order linear systems: Reachability and feedback invariants

We consider l-order linear control systems Σ with coefficients in a commutative ring R. The notion of reachability is studied for such systems and it is related to the reachability of the associated linearized system lin(Σ). We prove that reachability is a pointwise property, just as in the case of first order systems. The feedback equivalence of l-order linear control systems over a commutative ring is also studied. We introduce some feedback invariants that generalize the Hermida–Pérez–SánchezGiralda invariant modules Mi. To conclude we apply results in order to give classification results in low dimension.