How to Rewrite URL for Custom Controller Path in Magento 1.9

I have created a controller for my custom module. My controller path is like http://www.example.com/test/index/index which is displaying page correctly. I want to perform URL-rewrite for converting /test/index/index to /test.html

Based on the first answer, I have modified my code as below:

I tried to do something like following, in my config.xml

<frontend>
    <routers>
        <test>
            <use>standard</use>
            <args>
                <modules>
                    <module>Pfay_Test</module>
                    <frontName>test</frontName>
                </modules>
            </args>
        </test>
    </routers>
</frontend>

<global>
    <controller_front_init_routers>
        <observers>
            <test>  <!-- observer identifier -->
                <class>Pfay_Test_Controller_Router</class>
                <method>initControllerRouters</method>
            </test>
        </observers>
    </controller_front_init_routers>

</global>

In /app/code/local/Pfay/Test/Controller/Router.php

<?php
     class Pfay_Test_Controller_Router extends  Mage_Core_Controller_Varien_Router_Abstract{
/**
 * Initialize Controller Router
 *
 * @param Varien_Event_Observer $observer
 */

public function initControllerRouters($observer){
    $front=$observer->getEvent()->getFront();
    $front->addRouter('test',$this);

}


/* validate and modify the  request
 *  Params Zend_Controller_Request_Htt
 */
public function match(Zend_Controller_Request_Http $request){

    /* If Magento Magento is not install then 
     * redirect to installer url
     */
    If(!Mage::isInstalled()):
        Mage::app()->getFrontController()->getResponse()
            ->setRedirect(Mage::getUrl('install'))
            ->sendResponse();
        exit;

    endif;
    $requestPathInfo=trim($request->getPathInfo(),'/');
    Mage::log('aaa'.$requestPathInfo.'StoreId'.Mage::app()->getStore()->getId(), null, 'logfile.log');
    /* check -review-form not exit
     * then immediate return false
     */
    if($requestPathInfo!='test.html'):
        return  false;
    endif;


    $request->setModuleName('test')
        ->setControllerName('index')
        ->setActionName('index');
    $request->setAlias(
        Mage_Core_Model_Url_Rewrite::REWRITE_REQUEST_PATH_ALIAS,
        'test.html'
    );


    return  true;
  }
 }

In /app/code/local/Pfay/Test/Model/Observer.php

<?php
class Pfay_Test_Model_Observer{

public function add($observer){

    $identifier=$observer->getEvent()->getCondition();
    Mage::log('aaa', null, 'logfile.log');

     }

   }

But when I type http://www.example.com/test.html , it is still showing 404 error.Can anybody hint out where it is going wrong?

I am using Magento 1.9, Apache 2.4 and mod_rewrite is enabled.