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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. [ABSTRACT FROM AUTHOR]

In this note, we discuss the modeling and control of a class of Itô stochastic networked control systems (NCSs) with packet dropouts that are subject to time-varying sampling. The system under consideration is first modeled as a continuous-time system with input delay that is subject to double randomness via the input-delay approach. Then, by assuming the packet drop rate and recurring to the celebrated formula of total probability, an equivalent model which takes full advantage of probability distribution characteristics of both packet dropouts and sampling periods is established. In particular, the probability distribution values of the stochastic delay taking values in two given intervals can be explicitly obtained, which is of crucial importance to model and analyze the actual problem in NCSs. Based on that, robustly exponentially mean-square stability of the system with an $H_\infty$ performance is guaranteed, an $H_\infty$ controller design procedure is then proposed. Finally, a numerical simulation example is exploited to show the effectiveness and applicability of the results derived and some less conservative results are obtained. [ABSTRACT FROM AUTHOR]