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This work focuses on the invariance of important properties betweencontinuous and discrete models of systems which can be useful in the controldesign of large-scale systems and their software implementations. Inparticular, this paper discusses the relationships between the QSRdissipativity of a continuous state dynamical system and of its abstractionsobtained through approximate input-output simulation relations. First,conditions to guarantee the dissipativity of the continuous system from itsabstractions are provided. The reverse problem of determining the Q, S and Rdissipativity matrices of the abstract system from that of the continuoussystem is also considered. Results characterizing the change in thedissipativity matrices are provided when the system abstraction is obtained.Since, under certain conditions, QSR dissipative systems are known to bestable, the results of this paper can be used to construct stable systemabstractions as well. In the second part of this paper, we analyze thedissipativity of the approximate feedback composition of a continuous dynamicalsystem and a discrete controller. We present illustrative examples todemonstrate the results of this paper.

Dissipativity of system abstractions obtained using approximate input-output simulation