Easier way to upgrade your cluster is via portal or Azure CLI.
During the upgrade, platform will pick a node, cordon and drain the node and replace that nod with the new version. This will happen in a sequence for all the nodes.
If there is a failure during that process, upgrade stops. Its better to pick a non business hour for upgrades.
While upgrading you can move to the next minor version. You can't jump versions. So if you want to move from 1.11 to 1.13, you need to do two upgrades. One from 1.11 to 1.12 and, the next one from 1.12 to 1.13
This document explains the process of upgrading a cluster clearly. Please go through that and let me know if you face any issues.
Source : MSDN Thread Link