Stabilization of Sampled-Data Systems With Noisy Sampling Intervals and Packet Dropouts via a Discrete-Time Approach

In real-world applications, sampled-data systems are often subject to undesirable physical constraints, which results in noisy sampling intervals that fluctuate around an ideal sampling period based on certain probability distribution. In the presence of noisy sampling intervals, this article is con...

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Bibliographic Details
Published in:IEEE transactions on automatic control 2022-06, Vol.67 (6), p.3204-3211
Main Authors: Hu, Zhipei, Ren, Hongru, Deng, Feiqi, Li, Hongyi
Format: Article
Language:English
Subjects:
Confluent Vandermonde matrix
Control systems design
Convolution
convolution formula
Data systems
Discrete time systems
Dropouts
Feedback control
Intervals
law of total expectation
Mathematical analysis
Noise measurement
noisy sampling intervals
packet dropouts
Probability distribution
Random variables
Sampled data systems
Stability analysis
Stabilization
Stochastic systems
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Summary:In real-world applications, sampled-data systems are often subject to undesirable physical constraints, which results in noisy sampling intervals that fluctuate around an ideal sampling period based on certain probability distribution. In the presence of noisy sampling intervals, this article is concerned with the stabilization problem for a class of sampled-data systems with successive packet dropouts. First, the relationship between two adjacent update times of zero-order hold is established. Then, by discrete-time approach, an equivalent discrete-time stochastic system is introduced. By the law of total expectation, together with confluent Vandermonde matrix, convolution formula, and Kronecker product operation, the mathematical expectation of a product of three matrices, including the system matrix and its transpose, is calculated. Based on this, a stabilization controller is designed such that the closed-loop system is stochastically stable. Finally, an illustrative example is provided to verify the effectiveness of the proposed design approach.
ISSN:0018-9286
1558-2523
DOI:10.1109/TAC.2021.3096925