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, k₂)and a pulse transfer functionG^{}(z), isRe [(1+X^{}(z)+Y^{}(z))(G^{}(z)+I/k₂)]≥0forzon the unit circle, wherex(i) ≤ 0fori<0andx(i)=0fori>0, y(i) ≤ 0fori≥0andy(i)=0fori<0, andΣmin{i=-∞}max{+∞} \|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.