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In this paper, some results on the complete convergence for randomly weighted sums of widely orthant-dependent (WOD, for short) random variables are established under some general conditions, extending the corresponding ones obtained in the literature. By using the results that we presented, we further investigate the convergence of the state observers of linear-time-invariant systems based on WOD errors.

Complete convergence for randomly weighted sums of random variables and its application in linear-time-invariant systems