Abstract
This work is concerned with the problem for stochastic genetic regulatory networks (GRNs) subject to mixed time delays via passivity control in which mixed time delays consist of leakage, discrete, and distributed delays. The main aim of this paper is constructing a passivity-based criteria under impulsive perturbations such that the proposed GRNs are stochastically stable. Based on the Lyapunov functional method and Jensen’s integral inequality, we obtain a new set of novel passivity based delay-dependent sufficient condition in the form of LMIs, which can be determined via existing numerical software. Finally, we propose numerical simulations to show the efficiency of the proposed method.
Highlights
The regulatory networks have become an inevitable and a thriving field of research in the most acclaimed biomedical and biological scientific sectors [1]
To the best of authors’ knowledge, there is no literature on the passivity of stochastic genetic regulatory networks (GRNs) with leakage delays and impulsive perturbations, which encourages the current study
The novelty of the results in this paper pays more attention to the impulsive effects and leakage delays appearing in the stochastic genetic networks and the relevant passivity analysis with respect to the given time interval, and the main result of this paper is more general
Summary
The regulatory networks have become an inevitable and a thriving field of research in the most acclaimed biomedical and biological scientific sectors [1]. The problem of passivity control of recurrent neural networks subject to time delays and impulse perturbations is reported in [18]. Yang et al [19] investigated the result of passivity condition of neural networks with respect to distributed and discrete delays.
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