A system has a mobile robot for autonomously performing activities and a statically fitted alarm installation for monitoring an area. Accordingly, the robot and the alarm installation communicate with one another via a communication link. The mobile self-propelled robot uses a map of the environment to navigate across a floor space through at least a portion of the area and to locate its position on the map. Triggering of an alarm by the alarm installation is prevented when the robot moves into the area to be monitored. The triggering of the alarm by the alarm installation is made possible again when the robot moves out of the area to be monitored.