Distributed $H_\infty$ Filtering for Switched Stochastic Delayed Systems Over Sensor Networks With Fading Measurements

This paper is concerned with the problem of distributed <inline-formula> <tex-math notation="LaTeX">${H}_{{\infty }}$ </tex-math></inline-formula> filtering for switched stochastic time-delay systems with fading measurements over sensor networks. The underlying target plants are subject to fading measurements where the fading rates are described by continuous-time random variables with known statistical properties dependent on the system modes. The adjacency matrices characterizing the topology of the sensor networks are also allowed to be mode-dependent. Based on the multiple Lyapunov functional approach and average dwell-time concept, the distributed <inline-formula> <tex-math notation="LaTeX">${H}_{{\infty }}$ </tex-math></inline-formula> filter is designed by means of the convex optimization scheme. A dedicated technique is developed via a simple algebraic equality in order to avoid solving a transcendental equation used in the existing results. With the designed filter, the error dynamics of the state estimation is guaranteed to have the mean-square exponential stability with a prescribed <inline-formula> <tex-math notation="LaTeX">${H}_{{\infty }}$ </tex-math></inline-formula> disturbance attenuation level. Finally, a numerical example is used to demonstrate the effectiveness of the method.