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, 2012. Note: Submitted.Keyword(s): contractive systems, 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. E.D. Sontag. Contractive systems with inputs. In Jan Willems, Shinji Hara, Yoshito Ohta, and Hisaya Fujioka, editors, Perspectives in Mathematical System Theory, Control, and Signal Processing, pages 217-228. Springer-verlag, 2010. [PDF] Keyword(s): contractive systems. Abstract:

   Contraction theory provides an elegant way of analyzing the behaviors of systems subject to external inputs. Under sometimes easy to check hypotheses, systems can be shown to have the incremental stability property that all trajectories converge to a unique solution. This property is especially interesting when forcing functions are periodic (a globally attracting limit cycle results), as well as in the context of establishing synchronization results. The present paper provides a self-contained introduction to some basic results, with a focus on contractions with respect to non-Euclidean metrics.




3. 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, systems biology, biochemical 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 a fixed limit cycle. 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, systems biology, biochemical networks, synchronization. Abstract:

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

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