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

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2 Author(s)
O'Shea, R. ; US Steel Applied Research Laboratories, Monroeville, PA, USA ; Younis, M.

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})]\geq 0 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\geq 0 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.

Published in:

Automatic Control, IEEE Transactions on  (Volume:12 ,  Issue: 6 )