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| Stabilizability of minimum-phase systems with colored multiplicative uncertainty |
| JunhuiLi1,JieyingLu1,WeizhouSu1 |
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| (1 School of Automation Science and Engineering, South China University of Technology, Wushan, Guangzhou 510641, Guangdong, China) |
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| 摘要: |
| This work addresses the mean-square stability and stabilizability problem for minimum-phase multi-input and multi-output
(MIMO) plant with a novel colored multiplicative feedback uncertainty. The proposed uncertainty is generalization of the i.i.d.
multiplicative noise and assumed to be a stochastic system with random finite impulse response (FIR), which has advantage on
modeling a class of network phenomena such as random transmission delays. A concept of coefficient of frequency variation
is developed to characterize the proposed uncertainty. Then, the mean-square stability for the system is derived, which is a
generalization of the well-known mean-square small gain theorem. Based on this, the mean-square stabilizability condition is
established, which reveals the inherent connection between the stabilizability and the plant’s unstable poles and the coefficient
of frequency variation of the uncertainty. The result is verified by a numerical example on the stabilizability of a networked
system with random transmission delay as well as analog erasure channel. |
| 关键词: Mean-square stability · Mean-square stabilizability · Colored multiplicative noise · Networked control system |
| DOI：https://doi.org/10.1007/s11768-022-00108-9 |
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| 基金项目:This work was supported by the National Natural Science Foundation of China (Nos. 61933006 and 61673183). |
|
| Stabilizability of minimum-phase systems with colored multiplicative uncertainty |
| Junhui Li1,Jieying Lu1,Weizhou Su1 |
| (1 School of Automation Science and Engineering, South China University of Technology, Wushan, Guangzhou 510641, Guangdong, China) |
| Abstract: |
| This work addresses the mean-square stability and stabilizability problem for minimum-phase multi-input and multi-output
(MIMO) plant with a novel colored multiplicative feedback uncertainty. The proposed uncertainty is generalization of the i.i.d.
multiplicative noise and assumed to be a stochastic system with random finite impulse response (FIR), which has advantage on
modeling a class of network phenomena such as random transmission delays. A concept of coefficient of frequency variation
is developed to characterize the proposed uncertainty. Then, the mean-square stability for the system is derived, which is a
generalization of the well-known mean-square small gain theorem. Based on this, the mean-square stabilizability condition is
established, which reveals the inherent connection between the stabilizability and the plant’s unstable poles and the coefficient
of frequency variation of the uncertainty. The result is verified by a numerical example on the stabilizability of a networked
system with random transmission delay as well as analog erasure channel. |
| Key words: Mean-square stability · Mean-square stabilizability · Colored multiplicative noise · Networked control system |
