1. M. Marcondes de Freitas and E.D. Sontag. A small-gain theorem for random dynamical systems with inputs and outputs. SIAM J. Control and Optimization, 53:2657-2695, 2015. [PDF] Keyword(s): random dynamical systems, monotone systems, small-gain theorem, stochastic systems. Abstract:

   A formalism for the study of random dynamical systems with inputs and outputs (RDSIO) is introduced. An axiomatic framework and basic properties of RDSIO are developed, and a theorem is shown that guarantees the stability of interconnected systems.




2. M. Marcondes de Freitas and E.D. Sontag. Random dynamical systems with inputs. In C. Pötzsche and P. Kloeden, editors, Nonautonomous Dynamical Systems in the Life Sciences, Lecture Notes in Mathematics vol. 2102, pages 41-87. Springer-Verlag, 2013. [PDF] Keyword(s): random dynamical systems, monotone systems. Abstract:

   This work introduces a notion of random dynamical systems with inputs, providing several basic definitions and results on equilibria and convergence. It also presents a "converging input to converging state" result, a concept that plays a key role in the analysis of stability of feedback interconnections, for monotone systems.

1. M. Marcondes de Freitas and E.D. Sontag. A class of random control systems: Monotonicity and the convergent-input convergent-state property. In Proc. American Control Conference, pages 4564-4569, 2013. [PDF] Keyword(s): random dynamical systems, monotone systems.

1. M. Marcondes de Freitas and E.D. Sontag. Remarks on random dynamical systems with inputs and outputs and a small-gain theorem for monotone RDS. Technical report, http://arxiv.org/abs/1207.1690, July 2012. Keyword(s): random dynamical systems, monotone systems.

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