On gradient type adaptive filters with non-symmetric matrix step-sizes

In this contribution we provide a thorough stability analysis of gradient type algorithms with non-symmetric matrix step-sizes. We hereby extend existing analyses for symmetric matrix step-sizes and present several methods to derive step-size bounds. Although we can guarantee the I₂ - stability for such algorithms only under very restrictive conditions, we are able to proof convergence in the mean square sense under much more general conditions. Some of the derived step-size bounds turn out to very tight and allow for accurate algorithmic design.