Can bitcoin system get itself into resonant oscillations I assume that the PoW system has been designed in the way it controls itself. If the difficulty is too high and mining hash rate is low, then it takes more time to mine a block. The system detects that and adjusts the difficulty so the mining is easier. And vice versa. 

What if the decrease in difficulty would be too large? Then the block generation rate would rise quickly. The system would sense that and next raise of difficulty would be so large, that it would be greater than it was before it was lowered. Repeating this would cause the system to go into resonant oscillations and it would cause the difficulty to go into level that it would not be possible to mine a block and whole system would overload. 

Is the block mining system protected from such scenario?
Yes, there are protections.  

For example, Bitcoin restricts both the frequency and size of difficulty changes: the difficulty is re-assessed after each 2016 blocks, and is adjusted by no more than a factor of 4.  

The adjustment is also reactive rather than proactive: it looks at how fast the last 2016 blocks were generated, and sets the difficulty to the value that would have generated those blocks in 14 days, rather than trying to guess at a difficulty that will generate the next batch in 14 days.  Assuming that trends in available mining power are consistent over the short term (generally decreasing or generally increasing), this means that the adjustments are uniformly too small rather than too large, preventing oscillations and giving the historic trend that blocks are mined about every 9 minutes rather than the 10 minutes the system was intended to produce.