A semigroup approach to stochastic systems with input delay at the boundary

2021/12/27 by Said Hadd, Hadd, Said, Fatima Zahra Lahbiri +1
Mathematics · #93B28 #93C23 #93E03 #FOS: Mathematics #Optimization and Control (math.OC) #Probability (math.PR) #math.OC #math.PR #msc:93B28 #msc:93C23 #msc:93E03

paper · pdf · doi:10.48550/arxiv.2112.13636

17 pages

arxiv created 2021/12/27 · arxiv updated 2021/12/28

Abstract

This work focuses on the well-posedness of abstract stochastic linear systems with boundary input delay and unbounded observation operators. We use product spaces and a semigroup approach to reformulate such delay systems into free-delay distributed stochastic systems with unbounded control and observation operators. This gives us the opportunity to use the concept of admissible control and observation operators as well as the concept of Yosida extensions to prove the existence and uniqueness of the solution process and provide an estimation of the observation process in relation to initial conditions and control process. As an example, we consider a stochastic Schrödinger system with input delay.

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