Delay-Probability-Distribution-Dependent Stability of Uncertain Stochastic Genetic Regulatory Networks with Time-Varying Delays

Rakkiyappan, R.; Shanmugam, Lakshmanan; Balasubramaniam, P.

doi:10.1007/s00034-013-9595-2

Cited by 9 publications

(2 citation statements)

References 37 publications

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“…The existence of the time delays could affect the whole system performance and may lead to oscillation, divergence, and instability of the genetic networks. According to the occurrence way of time delays, they can generally be 2 Complexity classified into three types: interval time-varying delays [8,9], distributed delays [10], and random time delays [11,12]. In addition, gene regulation is an intrinsically noisy process due to intracellular and extracellular noise perturbations, which are derived from random births and deaths of individual molecules and environmental fluctuations.…”

Section: Introductionmentioning

confidence: 99%

Design of Nonfragile State Estimator for Discrete-Time Genetic Regulatory Networks Subject to Randomly Occurring Uncertainties and Time-Varying Delays

2017

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We deal with the design problem of nonfragile state estimator for discrete-time genetic regulatory networks (GRNs) with timevarying delays and randomly occurring uncertainties. In particular, the norm-bounded uncertainties enter into the GRNs in random ways in order to reflect the characteristic of the modelling errors, and the so-called randomly occurring uncertainties are characterized by certain mutually independent random variables obeying the Bernoulli distribution. The focus of the paper is on developing a new nonfragile state estimation method to estimate the concentrations of the mRNA and the protein for considered uncertain delayed GRNs, where the randomly occurring estimator gain perturbations are allowed. By constructing a LyapunovKrasovskii functional, a delay-dependent criterion is obtained in terms of linear matrix inequalities (LMIs) by properly using the discrete-time Wirtinger-based inequality and reciprocally convex combination approach as well as the free-weighting matrix method. It is shown that the proposed method ensures that the estimation error dynamics is globally asymptotically stable and the desired estimator parameter is designed via the solutions to certain LMIs. Finally, we provide two numerical examples to illustrate the feasibility and validity of the proposed estimation results.

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Section: Introductionmentioning

confidence: 99%

Design of Nonfragile State Estimator for Discrete-Time Genetic Regulatory Networks Subject to Randomly Occurring Uncertainties and Time-Varying Delays

2017

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“…Authors in [26] have applied integral inequality approach to reduce the conservatism of linear matrix inequalities. Recently, the stochastic stability of GRNs random delays are investigated in [27,28]. The obtained linear matrix inequalities are dependent on delay probability distributions.…”

Section: Introductionmentioning

confidence: 99%