As an economics major in university (haven't done VCE Economics), I've actually never heard of the term persuasion myself, but what you've described is what sounds a lot like how the RBA's credibility has a strong effect on the market interest rates.
If the market expects the RBA to act in a particular way (which can be communicated through their press releases), then this will cause the market to push rates in that direction without an official rate change. This happens because the press releases give information about what the RBA will do, and in anticipation of the rate change.
How this works:
If the market expects the RBA to increase rates (perhaps the RBA is quoting inflationary pressures), then borrowers have an incentive to borrow now (before rates rise), pushing up the interest rates to what the market is expecting the RBA to increase them to in the future.
On the other hand, if the market expects the RBA to decrease rates (need monetary stimulus, for example), then lenders wish to lend their money at the higher current rate, pushing down the interest rates to what the market expects the RBA to drop them to in the future.
Hence, the RBA can use this persuasion to affect rates without actually changing the cash rate. But this can only work if what they say is credible. And if they fail to act in accordance to what they say, then they will lose credibility, and so their persuasiveness in the market will decline.
Hope that helped.