Laboratory for Control, Learning, and Systems Biology

quasimetric spaces

1995
  1. ▪E.D. Sontag, "An abstract approach to dissipation", In Proc.\ IEEE Conf.\ Decision and Control, New Orleans, Dec.\ 1995, IEEE Publications, 1995, pp. 2702–2703, 1995. pdf
    Full version, never submitted, is here: http://sontaglab.org/FTPDIR/dissipation.pdf
    quasimetric spaces · dissipative systems · nonlinear systems
    Abstract

    We suggest that a very natural mathematical framework for the study of dissipation -in the sense of Willems, Moylan and Hill, and others- is that of indefinite quasimetric spaces. Several basic facts about dissipative systems are seen to be simple consequences of the properties of such spaces. Quasimetric spaces provide also one natural context for optimal control problems, and even for "gap" formulations of robustness.