Stabilization for sampled-data systems under noisy sampling interval

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• 作者：Bo Shen^a ; ¹ ; ^{bo.shen@dhu.edu.cn" class="auth_mail" title="E-mail the corresponding author} ; Zidong Wang^b ; ^{Zidong.Wang@brunel.ac.uk" class="auth_mail" title="E-mail the corresponding author} ; Tingwen Huang^c ; ^{tingwen.huang@qatar.tamu.edu" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Matrix exponential ; Noisy sampling interval ; Sampled-data control systems ; Stochastic control ; Synthesis of stochastic systems
• 刊名：Automatica
• 出版年：2016
• 出版时间：January 2016
• 年：2016
• 卷：63
• 期：Complete
• 页码：162-166
• 全文大小：412 K

文摘

In engineering practice, the sampling interval for a sampled-data system often fluctuates around a nominal/ideal value based on certain probability distributions that can be specified a priori through statistical tests. In this paper, a fundamental stabilization problem is investigated for a class of sampled-data systems under noisy sampling interval. The stochastic sampled-data control system under consideration is first converted into a discrete-time system whose system matrix is represented as an equivalent yet tractable form via the matrix exponential computation. Then, by introducing a Vandermonde matrix, the mathematical expectation of the quadratic form of the system matrix is computed. By recurring to the Kronecker product operation, the sampled-data stabilization controller is designed such that the closed-loop system is stochastically stable in the presence of noisy sampling interval. Subsequently, a special case is considered where the sampling interval obeys the continuous uniform distribution and the corresponding stabilization controller is designed. Finally, a numerical simulation example is provided to demonstrate the effectiveness of the proposed design approach.