On ${\mathcal H}_{\infty }$ Finite-Horizon Filtering Under Stochastic Protocol: Dealing With High-Rate Communication Networks

This paper is concerned with the <inline-formula><tex-math notation="LaTeX">${\mathcal H}_{\infty }$</tex-math> </inline-formula> filtering problem for a class of time-varying nonlinear delayed system under high-rate communication network and stochastic protocol (SP). The communication between the sensors and the state estimator is implemented via a shared high-rate communication network in which multiple transmissions are generated between two adjacent sampling instants of sensors. At each transmission instant, only one sensor is allowed to get access to the communication network in order to avoid data collisions and the SP is employed to determine which sensor obtains access to the network at a certain instant. The mapping technology is applied to characterize the randomly switching behavior of the data transmission resulting from the utilization of the SP. The aim of the problem addressed is to design an estimator such that the <inline-formula><tex-math notation="LaTeX">${\mathcal H}_{\infty }$</tex-math></inline-formula> disturbance attenuation level is guaranteed for the estimation error dynamics over a given finite horizon. Sufficient conditions are derived for the existence of the finite-horizon filter satisfying the prescribed <inline-formula> <tex-math notation="LaTeX">${\mathcal H}_{\infty }$</tex-math></inline-formula> performance requirement, and the explicit expression of the time-varying filter gains is characterized by resorting to a set of recursive matrix inequalities. Simulation results demonstrate the effectiveness of the proposed filter design scheme.

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