Abstract
In a previous paper, sufficient conditions for exponential stability and instability in mean square of linear stochastic systems subject to state dependent disturbances were shown. It was also conjectured that these conditions are close to necessary and sufficient conditions for exponential stability and instability. In this note, however, it is shown that this conjecture does not hold precisely except for a special class of systems. Examples which disprove the necessity of these conditions are given.
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