We generalize the notion of relative degree for a controlled dynamical system (possibly, discrete). We show that the new notion of leading incomplete relative degree is uniquely determined for a broad class of "square" dynamical systems (i.e., systems with as many inputs as outputs), including controllable systems. If r is the vector of relative degree of a system in the classical sense, then it is so in the generalized sense as well. We indicate a constructive algorithm for computing the leading incomplete relative degree.
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