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Feedback limitations of nonlinear systems are investigated using the cheap control approach. The main result is that in the limit, when the control effort is free, the smallest achievable L/sub 2/ norm of the output is equal to the least amount of control energy (L/sub 2/ norm) needed to stabilize the unstable zero dynamics. This nonlinear result is structurally similar to an earlier linear result by Qiu and Davison (1993), which, in turn, is connected with a Bode-type integral derived by Middleton (1991).
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Seron et al. (1999) studied this question.
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