Stabilization for sampled-data systems under noisy sampling interval

Abstract

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.