HMM-based H∞ filtering for Markov jump systems with partial information and sensor nonlinearities

This work examines the H∞ filtering issue for Markov jump systems in the circumstances of partial information on Markov chain and randomly occurring sensor nonlinearities. The partial information considered in this work includes partial information on the Markov state, on transition probabilities and on detection probabilities. A hidden Markov model with partially known transition probabilities and detection probabilities is introduced to describe the above partial information phenomenon. The randomly occurring sensor nonlinearities considered in this work depend on the system operating mode. Based on the Lyapunov methodology and the introduced hidden Markov model, some effective H∞ performance analysis criteria are derived for the filtering error system under the circumstances of partial information and sensor nonlinearities. In addition, the design procedure of the desired hidden Markov model-based filter is established, and finally two examples are used to verify the theoretical results.