Compatibility of behavior interconnections

In this paper we discuss the concept of compatible behavior interconnections. We distinguish the case where all variables are available for interconnection (total interconnection) from the case where only a part of them are (partial interconnection). The main idea behind the notion of compatibility for total interconnection is causality of (the effect of) the interconnection. We also show that state variables are closely related with the concept of compatibility. The concept of compatibility has been introduced for linear behaviors. In this paper, we propose an extension for the existing concepts. Relations between the proposed concept and the existing ones are also explained.