  This paper exhibits the closed-loop design constraints using the non-analytic
function theory. First, the paper generalizes the sensitivity integral for
linear feedback systems with the non-analytic sensitivity function. Sensitivity
inequalities are determined by the integral relationships based on the presence
of non-minimum phase zeros and right half plane poles. These inequalities are
rephrased in plant parameter context, which must be satisfied by the feedback
design. That indicates the ability of controllers under the influence of input
disturbances and plant parameter variations. The paper then extends the
integral to the analytic sensitivity function of the augmented linear feedback
systems. This is useful to augment the ability of a linear feedback system to
handle input disturbances and plant uncertainties, via modified sensitivity
function theory. Numerical simulations are carried out to perform sensitivity
analysis on three chemical control systems. That describes the usefulness and
demonstrates the applicability of the result of this paper to examine and
augment the ability of linear feedback system.
