1. G. Russo, M. di Bernardo, and E.D. Sontag. A contraction approach to the hierarchical analysis and design of networked systems. IEEE Transactions Autom. Control, 58:1328-1331, 2013. [PDF] Keyword(s): contractions, contractive systems, matrix measures, logarithmic norms, synchronization, systems biology. Abstract:

   This paper studies networks of components, and shows that a contraction property on the interconnection matrix, coupled with contractivity of the individual component subsystems, suffices to insure contractivity of the overall system.




2. G. Russo, M. di Bernardo, and E.D. Sontag. Global entrainment of transcriptional systems to periodic inputs. PLoS Computational Biology, 6:e1000739, 2010. [PDF] Keyword(s): contractive systems, contractions, systems biology, reaction networks, gene and protein networks. Abstract:

   This paper addresses the problem of giving conditions for transcriptional systems to be globally entrained to external periodic inputs. By using contraction theory, a powerful tool from dynamical systems theory, it is shown that certain systems driven by external periodic signals have the property that all solutions converge to fixed limit cycles. General results are proved, and the properties are verified in the specific case of some models of transcriptional systems.

1. G. Russo, M. di Bernardo, and E.D. Sontag. Stability of networked systems: a multi-scale approach using contraction. In Proc. IEEE Conf. Decision and Control, Atlanta, Dec. 2010, pages FrB14.3, 2010. Keyword(s): contractive systems, contractions, systems biology, reaction networks, synchronization. Abstract:

   Preliminary conference version of ''A contraction approach to the hierarchical analysis and design of networked systems''.

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