Utilization of noise for the control of a class of non-linear systems

TL;DR

This paper explores how noise, specifically stochastic anti-resonance with state-multiplicative noise, can be used to control certain non-linear systems, extending existing stability conditions to more general models.

Contribution

It demonstrates that stochastic anti-resonance control, previously limited to sector-bounded systems, can be applied to more general nonlinear systems using linear matrix inequalities.

Findings

SAR can stabilize a broader class of nonlinear systems.

LMI conditions effectively characterize stochastic stability.

Noise-based control offers alternative strategies in engineering and biological systems.

Abstract

Utilization of noise for the control of a class of non-linear systems is presented. The application of state-multiplicative noise as a mean of control is far more limited then the use of standard determinis?tic gains. Nevertheless, so called Stochastic Anti Resonance (SAR) with state-multiplicative noise based control, do arise in a variety of situations such as in engineering applications, physics modelling, bi?ology, and models of visuo-motor tasks. Linear Matrix Inequalities based conditions from recent publications are reviewed, that character?ize stochastic stability of such nonlinear systems applying SAR. While those results dealt with systems that are, apriori, modelled using sec?tor bounded nonlinearities, we demonstrate that more general systems that can be approximated as such, can be also controlled using SAR.