How does international law function in the current system to provide stability?
International law functions in the current system to provide stability by encouraging an atmosphere of voluntary adherence to the law. This comes to shape the expectations of how various countries should act. Most countries then act in accordance with the expectations.
When countries agree to abide by international law, they are creating expectations. Of course, there is not international government that can compel them to adhere to their obligations. However, by agreeing, they have created the expectation that they will honor the agreement. As more and more countries do this, a broader expectation arises. It comes to be assumed that all countries will abide by international law. This assumption comes to have weight of its own. It creates a situation in which countries feel compelled to obey international law because that is what is expected of them. In this way, stability is encouraged.