How get $state with absolute URL in Angular

There is a data field named $uiView attached to the ui-view element, it contains the view name and the associated state. You can get the state like this:

elem.closest('[ui-view]').data('$uiView').state

or even

elem.inheritedData('$uiView').state

So, in your controller:

 .controller('State1Ctrl', function ($state) {
      console.log(elem.closest('[ui-view]').data('$uiView').state); // state1
      console.log($state.current.name)  ;//will give the state name as well.  
});  

UPDATE:

Your issue: https://github.com/angular-ui/ui-router/issues/1651

WORKAROUND:
ANGULAR-UI-ROUTER: Resolve state from URL

You can expose the internal state implementation by using the .decorator hook on $stateProvider. You can decorate any property of the state builder; somebody chose 'parent' arbitrarily.

app.config(function($stateProvider) { 
  $stateProvider.decorator('parent', function (internalStateObj, parentFn) {
     // This fn is called by StateBuilder each time a state is registered

     // The first arg is the internal state. Capture it and add an accessor to public state object.
     internalStateObj.self.$$state = function() { return internalStateObj; };

     // pass through to default .parent() function
     return parentFn(internalStateObj); 
  });
});

Now you can access the internal state object using .$$state(), e.g.

var publicState = $state.get("foo");
    var privateInternalState = publicState.$$state();
    //Second, loop over each state in $state.get() and test them against your URL fragment.

    angular.forEach($state.get(), function(state) { 
      var privatePortion = state.$$state();
      var match = privatePortion.url.exec(url, queryParams);
      if (match) console.log("Matched state: " + state.name + " and parameters: " + match);
    });