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1. Marcondes de Freitas, Michael. A class of input/output random systems: monotonicity and a small-gain theorem.

Degree: PhD, Mathematics, 2014, Rutgers University

URL: https://rucore.libraries.rutgers.edu/rutgers-lib/45341/

We expand upon the theory of random dynamical systems (RDS) of L. Arnold, developing a theory of random dynamical systems with inputs and outputs (RDSIO)—an abstract framework for the treatment of noise-driven systems subject to stochastic inputs and yielding random outputs. This development allows for one to study both autonomous RDS and proper RDSIO as the feedback interconnection of smaller random input/output modules. As “proof of concept,” we prove a small-gain theorem for autonomous RDS which can be realized as the feedback interconnection of monotone RDSI with monotone or anti-monotone outputs. This result gives sufficient conditions for autonomous RDS to possess unique, globally attracting equilibria—the RDS in question need not be itself monotone.

Subjects/Keywords: Random dynamical systems; Monotonic functions

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APA (6^{th} Edition):

Marcondes de Freitas, M. (2014). A class of input/output random systems: monotonicity and a small-gain theorem. (Doctoral Dissertation). Rutgers University. Retrieved from https://rucore.libraries.rutgers.edu/rutgers-lib/45341/

Chicago Manual of Style (16^{th} Edition):

Marcondes de Freitas, Michael. “A class of input/output random systems: monotonicity and a small-gain theorem.” 2014. Doctoral Dissertation, Rutgers University. Accessed January 22, 2021. https://rucore.libraries.rutgers.edu/rutgers-lib/45341/.

MLA Handbook (7^{th} Edition):

Marcondes de Freitas, Michael. “A class of input/output random systems: monotonicity and a small-gain theorem.” 2014. Web. 22 Jan 2021.

Vancouver:

Marcondes de Freitas M. A class of input/output random systems: monotonicity and a small-gain theorem. [Internet] [Doctoral dissertation]. Rutgers University; 2014. [cited 2021 Jan 22]. Available from: https://rucore.libraries.rutgers.edu/rutgers-lib/45341/.

Council of Science Editors:

Marcondes de Freitas M. A class of input/output random systems: monotonicity and a small-gain theorem. [Doctoral Dissertation]. Rutgers University; 2014. Available from: https://rucore.libraries.rutgers.edu/rutgers-lib/45341/