Stabilization of hybrid stochastic differential equations by delay feedback control based on discrete-time observations

Chen, Xing and Li, Xiaoyue and Mao, Xuerong (2024) Stabilization of hybrid stochastic differential equations by delay feedback control based on discrete-time observations. Numerical Algebra, Control and Optimization. (In Press)

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Abstract

Response lags are necessary for most physical systems. For the sake of saving time and costs, the main aim of this paper is to design the feedback control term based on the response lags varying in a certain interval and the discrete-time observations of both the system states and the Markovian states to stabilize the controlled hybrid systems. The control principles are established, which permit the control function only depends on the partial information of the states and the modes. The upper bound on the sum of the upper bound Τ̅ of response lags, and the duration Ƭ between two consecutive observations is obtained. Some examples and numerical experiments are given to illustrate our theory.

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