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