A remark on conditioned invariance in the behavioral approach

In this paper a definition for the property of behavioral invariance is proposed with the purpose of generalizing the state space geometric approach to the behavioral setting. Based on this notion together with the well-known notion of behavioral observer, a definition of conditioned invariance is also presented. The results obtained for the characterization of the defined properties put into evidence some problems that, in our opinion, should deserve attention. This could serve as a starting point for a discussion on the foundations of an analogue of the geometric theory within the behavioral setting.