Mixed H∞ and passivity state estimation for two-time-scale semi-Markov jump coupled neural networks under analog fading channels

In this work, the state estimation issue for the two-time-scale semi-Markov jump coupled neural networks is addressed, in which the information of the system is transmitted through analog fading channels. A singular perturbation parameter is introduced to indicate the two-time-scale characteristics of semi-Markov jump coupled neural networks. Different from the existing Markov processes, this work uses the semi-Markov processes to model the jumping behavior, and further eliminates the restriction of the sojourn time probability distribution. Then, the Lyapunov function is considered to be related to singular perturbation parameters, sojourn times and system modes. Meanwhile, the mean square index stability criterion is introduced. Based on the criterion, the systems are mean square exponentially stable with the given mixed $H_{\infty }$ and passivity performance index by using the designed state estimation law. Finally, an illustrative example is used to show the design state estimation law is effective.