If you have a user control in your aspx page, and also the tab control is in the same aspx page, then you need to access the placed user control in tab load eventand not instantiate a new user control. Let's say the user control in aspx page has an id of userControl1, then the below code should work. Of course, this.userControl1.SystemName would only have a value if the dropdown in user control has an item selected.
Also, the dropdown selected index changed event should be defined within the user control that you have created. Once you place the user control in the aspx, then this code you have in the user control will automatically execute at the right time, which in this case is when the selected item changes in the dropdown.
protected void mainTabStrip_Load(object sender, EventArgs e)
{
string sysName = this.userControl1.SystemName;
}