Reduction of hyperoutput systems to a form with relative degree

We consider a notion of relative degree for hyperoutput systems (i.e. the systems that has more outputs than inputs). Relative degree conditions are restrictive (the same is true for a square systems - the systems that have the same number of inputs and outputs), furthermore, these conditions are not invariant under output change. We consider a problem of reducing a hyperoutput system to a form with relative degree. To solve the problem we indroduce generalizations of relative degree, similar to the square-system's case. Using these generalization we solve the problem.