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Delay Feedback Control for Switching Diffusion Systems Based on Discrete-Time Observations / Xiaoyue Li, Xuerong Mao, Denis S. Mukama, Chenggui Yuan

SIAM Journal on Control and Optimization, Volume: 58, Issue: 5, Pages: 2900 - 2926

Swansea University Author: Chenggui Yuan

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DOI (Published version): 10.1137/20m1312356

Abstract

Since response lags are required by most of physical systems and play a key role in the feedback control, the aim of this paper is to design delay feedback control functions based on the discrete-time observations of the system states and the Markovian states in order for the controlled switching di...

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Published in: SIAM Journal on Control and Optimization
ISSN: 0363-0129 1095-7138
Published: Society for Industrial & Applied Mathematics (SIAM) 2020
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URI: https://cronfa.swan.ac.uk/Record/cronfa57822
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Abstract: Since response lags are required by most of physical systems and play a key role in the feedback control, the aim of this paper is to design delay feedback control functions based on the discrete-time observations of the system states and the Markovian states in order for the controlled switching diffusion system (SDS) to be exponentially stable in $p$th moment and probability one as well as stable in $H_\8$. The main methods are the strong ergodicity theory of Markov chains and asymptotic analysis of stochastic functional differential equations (SFDEs). For the sake of saving time and costs the feedback control based on discrete-time observations is used to stabilize the switching diffusion systems.The designed control principles are implementable to stablize quasi-linear and highly nonlinear SDSs. For quasi-linear SDSs the criteria are sharp that under the control with high strength the controlled SDSs will be stable (bounded) while under the weaker control they will be unstable (unbounded) in mean square. The sample and moment Lyapunov exponents are estimated which have close relationship with the time delays.
Keywords: Brownian motion, Markov chain, Stochastic functional differential equations, Exponential stability, Moment boundedness, Lyapunov functional
College: College of Science
Issue: 5
Start Page: 2900
End Page: 2926