In order to make it work, you need to make the following changes:

/// <reference path="../scripts/typings/angularjs/angular.d.ts" />
/// <reference path="secondController.ts" />
/// <reference path="../scripts/typings/angularjs/angular-route.d.ts" />
module myApp {
export class Config {
  constructor($routeProvider: ng.route.IRouteProvider) {
     $routeProvider.when("/add", { templateUrl: "test.html", controller: "CategoryCtrl" })
        .when("/add2", { templateUrl: "test.html", controller: "secondController" })
        .otherwise({ redirectTo: '/list' });
  }
}
Config.$inject = ['$routeProvider'];
export class CategoryCtrl {
  constructor($window) {
     $window.alert("Hi from CategoryCtrl");
  }
}
CategoryCtrl.$inject = ['$window'];
export var app = angular.module("myApp", ['ngRoute']);
app.config(Config);
app.controller('CategoryCtrl', CategoryCtrl);

}

As you can see, I have removed the following line

app.controller('secondController', secondController);

I have also added this line

export var app = angular.module("myApp", ['ngRoute']);

This means that, the variable app will be accessible outside the module.

Now in the other file, where you have the secondController, you need to add the following line at

myApp.app.controller('secondController', secondController);

This is how your secondController file should look like

module myApp {
    export class secondController {
      constructor($window) {
         $window.alert("Second Controller");
      }
    }

secondController.$inject = ['$window'];
myApp.app.controller('secondController', secondController);
}

In the code that you wrote previously, app.ts file contains "secondController", but it does not know what this variable is, as the SecondController.ts file has not been loaded yet.

Now what I did is, I have made the the variable app, public.

So now we can register the new controller after it has been defined.

To make your life easier, I would suggest you to do the same thing with CategoryCtrl as well. Take its definition out of the app.ts file, and into its own file. Then register it with angular just like I did in secondController.

In doing so, you can easily add multiple files and register them.