A Small-Gain Theorem for Random Dynamical Systems with Inputs and Outputs

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.

Monotone dynamical systems: Reflections on new advances & applications

“…It is preserved by the dynamics of the delayed repressilator. These models have also been extended to include stochastic parameter dependence in [16,60]. Parabolic partial differential equations generate infinite dimensional dynamical systems that may also be order preserving.…”

“…The results described above provide a small taste of the kind of results that have been established in monotone control theory. See [1,2,3,90,60] and the references therein for more.…”