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

• Published in: IEEE transactions on automatic control Vol. 67; no. 6; pp. 3204 - 3211
• Main Authors: Hu, Zhipei, Ren, Hongru, Deng, Feiqi, Li, Hongyi
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.06.2022; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• 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
• ISSN: 0018-9286; 1558-2523
• DOI: 10.1109/TAC.2021.3096925

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.