A frequency-time domain stability criterion for sampled-data systems

An improved sufficient condition developed for the asymptotic stability of a sampled-data system having a single monotonic nonlinearity, with a slope in the sector
(0, k_{2})
and a pulse transfer function
G^{\ast}(z)
, is
Re [(1+X^{\ast}(z)+Y^{\ast}(z))(G^{\ast}(z)+I/k_{2})]\geq0
for
z
on the unit circle, where
x(i) \leq 0
for
i<0
and
x(i)=0
for
i>0, y(i) \leq 0
for
i\geq0
and
y(i)=0
for
i<0
, and
\Sigma\min{i=-\infty}\max{+\infty} \|x(i) + y(i)\| < 1
. An improved frequency domain condition is also presented for the case of the nonlinearity being odd as well as monotonic.