Fixed mqtt subscription filter on sys $ topics

tests/components/mqtt/test_init.py

@@ -249,6 +249,40 @@ def test_subscribe_topic_level_wildcard_and_wildcard_no_match(self):
         self.hass.block_till_done()
         self.assertEqual(0, len(self.calls))
 
+    def test_subscribe_topic_sys_root(self):
+        """Test the subscription of $ root topics."""
+        mqtt.subscribe(self.hass, '$test-topic/subtree/on', self.record_calls)
+
+        fire_mqtt_message(self.hass, '$test-topic/subtree/on', 'test-payload')
+
+        self.hass.block_till_done()
+        self.assertEqual(1, len(self.calls))
+        self.assertEqual('$test-topic/subtree/on', self.calls[0][0])
+        self.assertEqual('test-payload', self.calls[0][1])
+
+    def test_subscribe_topic_sys_root_and_wildcard_topic(self):
+        """Test the subscription of $ root and wildcard topics."""
+        mqtt.subscribe(self.hass, '$test-topic/#', self.record_calls)
+
+        fire_mqtt_message(self.hass, '$test-topic/some-topic', 'test-payload')
+
+        self.hass.block_till_done()
+        self.assertEqual(1, len(self.calls))
+        self.assertEqual('$test-topic/some-topic', self.calls[0][0])
+        self.assertEqual('test-payload', self.calls[0][1])
+
+    def test_subscribe_topic_sys_root_and_wildcard_subtree_topic(self):
+        """Test the subscription of $ root and wildcard subtree topics."""
+        mqtt.subscribe(self.hass, '$test-topic/subtree/#', self.record_calls)
+
+        fire_mqtt_message(self.hass, '$test-topic/subtree/some-topic',
+                          'test-payload')
+
+        self.hass.block_till_done()
+        self.assertEqual(1, len(self.calls))
+        self.assertEqual('$test-topic/subtree/some-topic', self.calls[0][0])
+        self.assertEqual('test-payload', self.calls[0][1])
+
     def test_subscribe_special_characters(self):
         """Test the subscription to topics with special characters."""
         topic = '/test-topic/$(.)[^]{-}'