Passive filter design for periodic stochastic systems with quantized measurements and randomly occurring nonlinearities

In this paper, the passive filter is designed for periodic stochastic systems with quantized measurements and randomly occurring nonlinearities. According to the dynamic properties of periodic systems, an N-periodic density quantizer is proposed to make full use of the communication capacity. By using Bernoulli processes, a new model is introduced to describe the randomly occurring nonlinearities, where each component of the state appears nonlinearity independently, and they influence each other based on the coupling matrices B(k). A reduced-order filter is designed to reduce the computation burden. Then sufficient conditions are established to ensure that the filtering error system is stochastically stable and satisfies the passivity. Finally, the effectiveness of the proposed new design technique is illustrated via a numerical example.