Stabilization of stochastic functional systems via PI-type controls

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Zong, Xiaofeng and Hou, Xuping and Wu, Fuke and Mao, Xuerong (2025) Stabilization of stochastic functional systems via PI-type controls. IEEE Control Systems Letters, 9. pp. 2429-2434. ISSN 2475-1456 (https://doi.org/10.1109/lcsys.2025.3625473)

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Abstract

Motivated by the proportional integral (PI) control theory of deterministic systems, this letter aims to establish the PI-type control theory for stochastic systems, including the standard PI control and the proportional fragment-integral (PFI) control. For the standard PI control of stochastic functional systems (SFSs), the mean square and almost sure stabilization criteria are investigated, and then the explicit design of the proportional gain and the integral gain is obtained. It is revealed that the proportional gain matrix can be firstly designed and then the negative definite integral gain matrix can be determined based on the design of the proportional gain matrix. For the PFI control, the joint design of the proportional gain and the fragment-integral gain is proposed. It is shown that the fragment integral can work positively for the stabilization. Finally, the numerical methods are also proposed to approximate the two-type closed-loop SFSs and the simulation examples are given to confirm the theoretical results.

ORCID iDs

Zong, Xiaofeng, Hou, Xuping, Wu, Fuke and Mao, Xuerong ORCID logoORCID: https://orcid.org/0000-0002-6768-9864;
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