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Controllability of stochastic nonlinear oscillating delay systems driven by the Rosenblatt distribution

Part of: Functional-differential and differential-difference equations Control systems

Published online by Cambridge University Press:  03 March 2020

T. Sathiyaraj ,
JinRong Wang  and
D. O'Regan
T. Sathiyaraj
Affiliation:
Department of Mathematics, Guizhou University, Guiyang, Guizhou550025, P.R. China
JinRong Wang*
Affiliation:
Department of Mathematics, Guizhou University, Guiyang, Guizhou550025, P.R. China and School of Mathematical Sciences, Qufu Normal University, Qufu, Shandong273165, P.R. China ([email protected])
D. O'Regan
Affiliation:
School of Mathematics, Statistics and Applied Mathematics, National University of Ireland, Galway, Republic of Ireland
*
*Corresponding author.
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Abstract

In this paper, we study the controllability of second-order nonlinear stochastic delay systems driven by the Rosenblatt distributions in finite dimensional spaces. A set of sufficient conditions are established for controllability of nonlinear stochastic delay systems using fixed point theory, delayed sine and cosine matrices and delayed Grammian matrices. Furthermore, controllability results for second-order stochastic delay systems driven by Rosenblatt distributions via the representation of solution by delayed sine and cosine functions are presented. Finally, our theoretical results are illustrated through numerical simulation.

Keywords

Stochastic delay systemsDelayed perturbations matrixControllability

MSC classification

Primary: 34K50: Stochastic functional-differential equations
Secondary: 93C05: Linear systems
Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 151 , Issue 1 , February 2021 , pp. 217 - 239
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Copyright
Copyright © The Author(s), 2020. The Royal Society of Edinburgh

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