A generalized viewpoint of a criterion due to D. Mitra

D. Mitra [1] presented a criterion for the absolute stability of a class of discrete-time systems employing the saturation nonlinearity. He has discussed the application of his criterion exclusively for the case of saturation nonlinearity. The purpose of this paper is to extend the applicability of his criterion to cover a variety of the nonlinearity form including the saturation characteristic as a special case. To be specific, it is shown that the satisfaction of Mitra's criterion for some
\alpha_{r} > 0,\beta_{r}> 0, r = 1,2,\cdots,m
not only implies absolute stability for the saturation nonlinearity, but it also implies absolute stability for several other forms of the nonlinearity.