  Unlike the situation with gain and phase margins in robust stabilization, the
problem to determine an exact maximum delay margin is still an open problem,
although extensive work has been done to establish upper and lower bounds. The
problem is that the corresponding constraints in the Nyquist plot are frequency
dependent, and encircling the point $s=-1$ has to be done at sufficiently low
frequencies, as the possibility to do so closes at higher frequencies. In this
paper we present a new method for determining a sharper lower bound by
introducing a frequency-dependent shift. The problem of finding such a bound
simultaneously with gain and phase margin constraints is also considered. In
all these problems we take an analytic interpolation approach.
