$$H_{\infty }$$H∞ Filtering for Markov Jump Neural Networks Subject to Hidden-Markov Mode Observation and Packet Dropouts via an Improved Activation Function Dividing Method

This paper is devoted to investigating the $$H_{\infty }$$ filtering problem for Markov jump neural networks with hidden-Markov mode observation and packet dropouts, in which the information regarding to the Markov state can not be completely acquired. To address this circumstance, a hidden Markov model (HMM)-based technique is established. That is employing a detector to detect the information of the Markov state and then giving an estimated signal of the Markov state for the filter design. Some $$H_{\infty }$$ performance analysis criteria for filtering error systems and the corresponding HMM-based filter design procedure are given. An improved activation function dividing method (AFDM) is presented for neural networks to reduce the conservatism of the obtained results. The superiority of the improved AFDM and the validity of obtained results are verified by an illustrative example.