Answer: Unfortunately I am not certain which plant you have, based on the information in your question. There are actually some shrubby clematis, so that might be it. Here is a photo of one as an example.
There are some hydrangeas that have flat, four petaled purple or blue flowers, these surround a cluster of smaller flowers that seem not to open completely. Here is a photo as an example, there are many different Hydrangea serrata cultivars with purple flowers.
There are some blue to purple flowered rose of Sharon plants, such as Blue Bird, here is a photo -- the bloom flattens out somewhat although it has too many petals.
There are several purple or blue flowered tropical plants such as brunfelsia and tibouchina, however they too have more than four petals so I ruled them out as well.
I'm sorry I can't tell you specifically what you have. If none of these seem right, you might take some photos of the flower, the foliage, and the overall plant and ask your local county extension or perhaps at the botany department of a nearby college or university. I hope you find out what it is!
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