FDE-Dissipativity and its similarities with ISS systems

In this paper, a term of FDE-Dissipativity in delayed nonlinear system is introduced and explored. It is shown that the FDE-Dissipativity is a sufficient condition for output to be bounded. In special cases, FDE-Dissipativity will also implies Input to State Stability (ISS) for time delay systems. Moreover it is also shown that it has equivalent characteristics with non-delayed nonlinear systems, for instance, feedback interconnection of two FDE-Dissipative systems is also FDE-Dissipative and it is possible to reconstruct loop-transformation with property similar to non-delayed passive system. To achieve this goal an approach from dissipativity of functional differential equation is employed.