Robust H ∞ filtering for 2D systems with RON under the stochastic communication protocol

This study is concerned with the robust H ∞ filtering problem for two-dimensional (2D) systems in Roesser model with randomly occurring non-linearity (RON) and stochastic communication protocol (SCP). The introduced non-linearity is sector-like and governed by a random variable obeying the Bernoulli distribution law. The SCP is depicted by an independent and identically distributed sequence to schedule the signal transmission. The phenomenon of time delay is also taken into consideration. The aim of this study is to design a filter such that the augmented filtering error system satisfies a predefined H ∞ performance index. Sufficient condition is first given to ensure the robust stability of the augmented filtering error system via Lyapunov theory and stochastic analysis. Then, the result is extended to guarantee the H ∞ performance of the augmented system under SCP, where sufficient criterion related to the transmission probability is given in terms of matrix inequality. Moreover, the filter gains are explicitly designed which enable the system to achieve the H ∞ filtering performance. Finally, a numerical example is given to show the effectiveness of the proposed design method.