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

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Abstract
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 functionG^{\ast}(z), isRe [(1+X^{\ast}(z)+Y^{\ast}(z))(G^{\ast}(z)+I/k_{2})]\geq0forzon the unit circle, wherex(i) \leq 0fori0, y(i) \leq 0fori\geq0andy(i)=0fori<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.