H∞ Filtering for Discrete-Time Periodic Markov Jump Systems With Quantized Measurements: A New Packet Loss Compensation Strategy

The $H_{\infty }$ filtering problem for discrete-time periodic Markov jump systems with quantized measurements and packet loss compensation is addressed in this article. The stochastic packet loss phenomenon, which arises from the plant to the filter, obeys Bernoulli distribution. Then, aiming at the phenomenon that the system performance is degraded or even unstable due to packet loss, a new packet loss compensation strategy is proposed, which adopts the single exponential smoothing method. Considering the limited communication channel, a static logarithmic quantizer with mode-dependent property is used to quantify the measured output. Besides, since the system modes are not always fully available, a quantized periodic filter, which is partially mode-dependent, is constructed to guarantee that the filtering error system is stochastically stable. Furthermore, by constructing a periodic Lyapunov function with mode-dependent property, the existence conditions of periodic filter are presented. Eventually, to illustrate the usefulness of the proposed approach, a practical example of a boost converter is presented.