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THE ZERO DYNAMICS OF A NONLINEAR SYSTEM 1 Relative degree and local normal forms

The purpose of this Section is to show how single-input single-output nonlinear systems can be locally given, by means of a suitable change of coordinates in the state space, a “normal form” of special interest, on which several important properties can be elucidated. The point of departure of the whole analysis is the notion of relative degree of the system, which is formally described in the following way. The single-input single-output nonlinear system ẋ = f(x) + g(x)u y = h(x) (1)