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This paper is concerned with the problem of extended dissipativity analysis for delayed uncertain discrete-time singular neural networks (DTSNNs) having Markovian jump parameters and stochastic behavior. This paper demands to derive delay-dependent sufficient conditions such that the DTSNNs to be regular and causal, and is to find the stability nature and the robustness of the performance measures in the mean square sense. Based on Lyapunov–Krasovskii functional method and Cauchy–Schwartz-based summation inequality technique, a sufficient condition to guarantee an extended dissipativity performance and stability criterion for uncertain stochastic DTSNNs is presented in terms of linear matrix inequalities. Finally, numerical examples are provided to illustrate the advantages and improvements of the proposed method. [ABSTRACT FROM AUTHOR]

This paper is concerned with the mixed H∞ and dissipativity performance for Markovian jump neural networks with time delay in the leakage term and randomly occurring uncertainties. The randomly occurring uncertainties are assumed to be mutually uncorrelated Bernoulli-distributed white noise sequences. By introducing a triple-integrable term in the Lyapunov functional, the Wirtinger-based double-integral inequality is utilized to bound the derivative of the triple-integral term and then a sufficient condition is derived to ensure that the considered neural networks to be strict (Q,S,R)-γ-dissipative and passive. These conditions are presented in terms of linear matrix inequalities, which can be easily solved by using standard numerical software. Finally, numerical examples are given to show the effectiveness and the potential significance of the proposed results. [ABSTRACT FROM AUTHOR]

In this paper, the problem of robust state estimation for discrete-time stochastic Markov jump neural networks with discrete and distributed time-varying delays is investigated based on dissipativity and passivity theory. The parameters of the neural networks are subject to the switching from one mode to another according to a Markov chain. By using the Lyapunov-Krasovskii functional together with linear matrix inequality approach, a new set of sufficient conditions are derived for the existence of state estimator such that the error state system is strictly $$(\mathcal {Q}, \mathcal {S}, \mathcal {R})-\gamma $$ -dissipative. Finally, numerical examples are addressed to show the effectiveness of the proposed design method . [ABSTRACT FROM AUTHOR]