H∞H∞ filtering with stochastic sampling

This paper is concerned with the problem of H∞H∞ filtering for continuous-time systems under sampled measurements with probabilistic sampling. It is assumed that the occurrence probabilities of the sampling intervals are given constants and satisfy a Bernoulli distribution. Through a transformation of the discrete time instants, the filtering error system is formulated as a continuous-time system with delays and stochastic parameters. Then, H∞H∞ filter is designed such that the filtering error system is exponentially stable in the mean square, and the L2L2-induced gain from the noise signal to the estimation error is guaranteed to be less than a prescribed level. Finally, an example is given to show the effectiveness of the theoretical results.