Observer-based H∞ Control for Sampled-data System Under Stochastic Sampling

This study is concerned with the problem ofobserver-based $H_{\infty}$ control for sampled-data systems under stochastic sampling. An observer-based sampled-data control scheme is developed, in which the state of the system is sampled with a stochastic sampling interval following a certain probability density. Compared with the existing results, there are two main differences. One is that the eigenvalues of the system matrix are allowed to be zero. The other is that our result can be applied to the multivariable systems. With the help of the Kronecker product operation and the Vandermonde matrix, stochastic stability criteria are derived to ensure that the closed-loop system is exponentially stable in the mean square with a prescribed $H_{\infty}$ performance. Moreover, an $H_{\infty}$ controller design procedure is then proposed based on a cone complementarity linearization algorithm. Finally, the effectiveness of the proposed design method is demonstrated by a numerical example.

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