title: Energy-to-peak state estimation for Markov jump RNNs with time-varying delays via nonsynchronous filter with nonstationary mode transitions.
abstract: In this paper, the problem of energy-to-peak state estimation for a class of discrete-time Markov jump recurrent neural networks (RNNs) with randomly occurring nonlinearities (RONs) and time-varying delays is investigated. A practical phenomenon of nonsynchronous jumps between RNNs modes and desired mode-dependent filters is considered, and a nonstationary mode transition among the filters is used to model the nonsynchronous jumps to different degrees that are also mode dependent. The RONs are used to model a class of sector-like nonlinearities that occur in a probabilistic way according to a Bernoulli sequence. The time-varying delays are supposed to be mode dependent and unknown, but with known lower and upper bounds a priori. Sufficient conditions on the existence of the nonsynchronous filters are obtained such that the filtering error system is stochastically stable and achieves a prescribed energy-to-peak performance index. Further to the recent study on the class of nonsynchronous estimation problem, a monotonicity is observed in obtaining filtering performance index, while changing the degree of nonsynchronous jumps. A numerical example is presented to verify the theoretical findings.
authors.forename: Lixian
authors.initials: L
authors.lastname: Zhang
authors.forename: Yanzheng
authors.initials: Y
authors.lastname: Zhu
authors.forename: Wei Xing
authors.initials: WX
authors.lastname: Zheng
mesh_terms: D000465:Algorithms; D003198:Computer Simulation; D006801:Humans; D008390:Markov Chains; D008959:Models, Neurological; D016571:Neural Networks, Computer; D009474:Neurons; D017711:Nonlinear Dynamics; D013997:Time Factors