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State estimation for jumping recurrent neural networks with discrete and distributed delays
Zidong Wang1, Yurong Liu, Xiaohui Liu
1Department of Information Systems and Computing, Brunel University, Uxbridge, Middlesex, UB8 3PH, UK. Zidong.Wang@brunel.ac.uk
Summary
This study develops a novel method for state estimation in Markovian neural networks with time-delays. The approach ensures stable estimation error dynamics for these complex, mode-jumping systems.
Area of Science:
- Control Systems Engineering
- Computational Neuroscience
- Stochastic Systems
Background:
- Markovian neural networks (MNNs) are complex systems with finite modes that transition based on a Markov chain.
- These networks often exhibit discrete and distributed time-delays, complicating state estimation.
- Ensuring stability in the mean square for estimation errors is crucial for reliable MNN operation.
Purpose of the Study:
- To address the state estimation problem for MNNs with time-delays and Markovian jumping parameters.
- To design an estimator that guarantees globally asymptotically stable mean-square estimation error dynamics.
- To provide a systematic method for constructing such estimators.
Main Methods:
- Development of a linear matrix inequality (LMI) approach for state estimation.
- Derivation of existence conditions for the proposed estimator.
- Explicit characterization of the estimator's parameters.
Main Results:
- An effective LMI-based method is presented for state estimation in delayed MNNs.
- Conditions for the existence of a stable estimator are established.
- The method successfully estimates neuron states while ensuring stability of the estimation error.
Conclusions:
- The proposed LMI approach provides a robust solution for state estimation in MNNs with time-delays.
- The method's applicability is demonstrated through numerical examples.
- The results extend to traditional stability analysis of delayed MNNs with Markovian jumping parameters.
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