H∞ state estimation for two-dimensional systems with randomly occurring uncertainties and Round-Robin protocol

Abstract In this paper, the robust H∞ state estimator is designed for the two-dimensional (2-D) systems in Fornasini-Machesini second model under logarithmic quantization and Round-Robin protocol. The norm-bounded uncertainties are also involved in the considered system, which are governed by two stochastic variables satisfying the Bernoulli distribution. As a kind of static scheduling, the Round-Robin protocol assigns the communication access rights to the sensors in the chronological order. The aim of this paper is to design a state estimator so that the addressed estimation error system satisfies a predefined H∞ performance index. Sufficient conditions are given to ensure the 2-D augmented error system to be robustly stable via intensive stochastic analysis, then the results are further extended to achieve the robust H∞ stability for the augmented error system. Explicit expressions of the estimator gains are also given by solving certain matrix inequalities. Finally, a numerical example is presented to demonstrate the effectiveness of the proposed estimation scheme.

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