Stabilizing composite control for a class of linear systems modeled by singularly perturbed Ito differential equations

In this paper, the problem of robust H ∞ 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 (LMI) approach, sufficient conditions are obtained, which guarantee the robust mean-square exponential stability of the system with an H ∞ performance. Moreover, an H ∞ controller design procedure is then proposed. An illustrative example is included to demonstrate the effectiveness of the proposed techniques.