A tradeoff between disturbance attenuation and stability robustness

We consider a feedback system whose performance output differs from its measure output and show that, except in special cases, such a system will exhibit a tradeoff between disturbance response and stability robustness. The severity of this tradeoff is governed by a dimensionless plant parameter, and tends to be significant for systems with lightly damped zeros. The results are illustrated with the problem of noise cancellation in an acoustic duct.