Feedback limitations in nonlinear systems: from Bode integrals to cheap control

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).