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Robust sampled-data \(H_\infty \) control with stochastic sampling. (English) Zbl 1184.93039

Summary: The problem of robust \(H_\infty \) control is investigated for sampled-data systems with probabilistic sampling. The parameter uncertainties are time-varying norm-bounded and appear in both the state and input matrices. For the simplicity of technical development, only two different sampling periods are considered whose occurrence probabilities are given constants and satisfy Bernoulli distribution, which can be further extended to the case with multiple stochastic sampling periods. By applying an input-delay approach, the probabilistic sampling system is transformed into a continuous time-delay system with stochastic parameters in the system matrices. By linear matrix inequality approach, sufficient conditions are obtained, which guarantee the robust mean-square exponential stability of the system with an \(H_\infty \) performance. Moreover, an \(H_\infty \) controller design procedure is then proposed. An illustrative example is included to demonstrate the effectiveness of the proposed techniques.

MSC:

93B36 \(H^\infty\)-control
93C57 Sampled-data control/observation systems
93E03 Stochastic systems in control theory (general)
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