Dear Rodolfo, there are many research dealing with control design based on differential dissipativity. One of these papers that might be interesting is on following link:

http://focapo.cheme.cmu.edu/2012/proceedings/data/papers/047.pdf

Hope it will be helpfull!

Kind regards,

Ljubomir Jacic

Thaks prof Ljubomir, I know there are many research about passivity and dissipativity, but differential disipativity or passivity deal with differential geometric point of view, I is a new idea of Rodolphe Sepulchre and Arjan van der Schaft.

Dear Rodolfo,

Differential Dissipativity is a concept introduced by myself and Jean-Jacques Slotine in 2012, see here:

http://arxiv.org/abs/1209.4433

Previously, Jouffroy studied some special cases of this concept in his paper "A Simple Extension of Contraction Theory to Study Incremental Stability Properties", ECC 2003.

More recently Sepulchre, van der Schaft, and others have been investigating this concept as well.

It is based on the contraction theory developed by Lohmiller and Slotine and others. It extends contraction theory to input/output properties and more general feedback interconnections, along the same lines as dissipation inequalities and IQC extends Lyapunov theory.

There has not been much application in control design yet, but the idea has been used already for system identification, see here:

http://arxiv.org/pdf/1009.1670v1.pdf

Let me know if you have any questions about these techniques.

Ian

Note also that it is closely related (in some sense an infinitesimal version) of an old concept: incremental passivity, for which you should read the classic book of Desoer and Vidyasagar.

Thank you again prof. Ian, Now I am working deeper in this topic, and your previous answer has helped me.