We will begin with a review of Health Smart Homes (HSH) around the world before moving onto a description of our system, the HIS² or "Health Integrated Smart Home Information System", developed at the TIMC laboratory in Grenoble. We hypothesize that there is a connection between biological and social rhythms, behavior, and thus with physical activity which we can measure by observing a subject's displacements within the habitat. We created the term "activity circadian rhythms" (ACR) to refer to the behavioral measurement of patient activity inside the habitat. The HIS² system is made up of an external HIS² connected to the Internet and a local HIS², which is the object of our discussion here. The local HIS², using various types of sensors, is designed to monitor and, though the ACR calculations, self-learn the daily habits of a patient within the HIS², and thus to detect abnormal evolution of the patient's behavior over the long term. A simulation software has been developed to validate the system.