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Abstract This paper presents the problems of state space model identification of multirate processes with unknown time delay. The aim is to identify a multirate state space model to approximate the parameter-varying time-delay system. The identification problems are formulated under the framework of the expectation maximization algorithm. Through introducing two hidden variables, a new expectation maximization algorithm is derived to estimate the unknown model parameters and the time-delays simultaneously. The effectiveness of the proposed algorithm is validated by a simulation example. [ABSTRACT FROM AUTHOR]

Abstract: Two bilateral inequalities based on the Borel–Cantelli lemma and a non-negative sequence of bounded random variables were respectively obtained by . However, we observe that the upper bounds in the above cited references are greater than or equal to 1, so the upper bounds of these bilateral inequalities always hold true. In this note, we will extend the lower bound results on the assumptions that the random variables are neither non-negative nor bounded, which could be considered as a version of the Borel–Cantelli lemma with a random weight sequence. As an application, we also discuss the example given in and , and the best result is easily obtained for this example by taking the appropriate weight sequence. [Copyright &y& Elsevier]