Stabilization for sampled-data systems under noisy sampling interval

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 o...

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Bibliographic Details
Published in:Automatica (Oxford) Vol. 63; pp. 162 - 166
Main Authors: Shen, Bo, Wang, Zidong, Huang, Tingwen
Format: Journal Article
Language:English
Published: Elsevier Ltd 01.01.2016
Subjects:
Matrix exponential
Noisy sampling interval
Sampled-data control systems
Stochastic control
Synthesis of stochastic systems
Stochastic control
Synthesis of stochastic systems
Noisy sampling interval
Sampled-data control systems
Matrix exponential
ISSN:0005-1098, 1873-2836
Online Access:Get full text
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Summary: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.
ISSN:0005-1098
1873-2836
DOI:10.1016/j.automatica.2015.10.005