app.class.php

<?php
/**
 * Copyright (c) 2013 Roman Ožana (http://omdesign.cz)
 *
 * For the full copyright and license information, please view
 * the file license.txt that was distributed with this source code.
 *
 * @author Roman Ozana <ozana@omdesign.cz>
 * @method Homepage()
 * @method Homepage_actiom()
 */
class App extends Slim {

  public function __construct() {
    parent::__construct();
    $this->container->singleton(
			'mysuperclass', function ($container) {
				return new MySuperClass();
			}
		);
  }
	public function __call($name, $params) {
		return function () use ($name, $params) {
			list($class, $action) = explode('_', $name . '_handle'); // default method is handle

			$args = [];
			$class = new \ReflectionClass($class);
			$constructor = $class->getConstructor();
			foreach ($constructor->getParameters() as $param) {
				$args[] = ($param->name === 'app') ? $this : $this->container->get($param->name);
			}
			$controller = $class->newInstanceArgs($args);
			return call_user_func([$controller, $action], func_get_args() + $params);
		};
	}
}

homepage.php

<?php
class Homepage {

	public $app;
	public $router;
	public $mysuperclass;

	public function __construct(\App $app, \Slim\Router $router, \MySuperClass $mysuperclass) {
		$this->app = $app;
		$this->router = $router;
		$this->mysuperclass = $mysuperclass;
	}

	public function handle() {
		var_dump($this->app); // have something
	}
	
	public function action() {
	 // call action
	}
}

index.php

<?php
$app = new App();
$app->map('/', $app->Homepage())->via('GET', 'POST');
$app->map('/action', $app->Homepage_action())->via('GET', 'POST');
$app->run();