Delay feedback control for switching diffusion systems based on discrete-time observations

Xiaoyue Li, Xuerong Mao, Denis S. Mukama, Chenggui Yuan

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Abstract

For the sake of saving time and costs the feedback control based on discrete-time observations is used to stabilize the switching diffusion systems. Response lags are required by most 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 the pth moment with probability one as well as stable in H∞. 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 the mean square. The sample and moment Lyapunov exponents are estimated which have a close relationship to the time delays.

Original languageEnglish
Pages (from-to)2900–2926
Number of pages27
JournalSIAM Journal on Control and Optimization
Volume58
Issue number5
Early online date17 Sep 2020
DOIs
Publication statusE-pub ahead of print - 17 Sep 2020

Keywords

  • Brownian motion
  • Markov chain
  • stocastic functional differential equations
  • exponential stability
  • moment boundedness
  • Lyapunov functional

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