Robust stability for genetic regulatory networks with linear fractional uncertainties

Zhang, Wenbing; Fang, Jian‐an; Tang, Yang

doi:10.1016/j.cnsns.2011.09.026

Cited by 31 publications

(36 citation statements)

References 25 publications

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“…Moreover, both the intrinsic noise derived from the random births and deaths of individual molecules and the extrinsic noise due to environment fluctuations make the gene regulation process 2 Mathematical Problems in Engineering an intrinsically noisy process [59]. Thus, many researches aimed at the robust stability analysis of the GRNs in consideration of those noises [37][38][39][40][41][42][43][44][45][46]. Also, some results have considered both the uncertainties and the noises [47][48][49][50][51][52].…”

Section: Introductionmentioning

confidence: 99%

Stability Analysis of Delayed Genetic Regulatory Networks via a Relaxed Double Integral Inequality

Zhu

et al. 2017

Mathematical Problems in Engineering

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Time delay arising in a genetic regulatory network may cause the instability. This paper is concerned with the stability analysis of genetic regulatory networks with interval time-varying delays. Firstly, a relaxed double integral inequality, named as Wirtinger-type double integral inequality (WTDII), is established to estimate the double integral term appearing in the derivative of LyapunovKrasovskii functional with a triple integral term. And it is proved theoretically that the proposed WTDII is tighter than the widely used Jensen-based double inequality and the recently developed Wiringter-based double inequality. Then, by applying the WTDII to the stability analysis of a delayed genetic regulatory network, together with the usage of useful information of regulatory functions, several delay-range-and delay-rate-dependent (or delay-rate-independent) criteria are derived in terms of linear matrix inequalities. Finally, an example is carried out to verify the effectiveness of the proposed method and also to show the advantages of the established stability criteria through the comparison with some literature.

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Section: Introductionmentioning

confidence: 99%

Stability Analysis of Delayed Genetic Regulatory Networks via a Relaxed Double Integral Inequality

Zhu

et al. 2017

Mathematical Problems in Engineering

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“…In view of the extra fractional-order variables, the application of fractional calculus has many advantages superior to that of traditional integer calculus, such as more flexibility, freedom, best fit, and optimization techniques and so on. Therefore, many scientists have attempted to broaden the scope of fundamentals and theorems from integer order systems into fractional ones in biomedical applications [2,3], chaotic systems [4,5], signal processing [6], control design [7], and more. More specifically, the applications of fractional calculus on the filter design have yielded much recent progress in theory [8][9][10], noise analysis [11] and stability analysis [12].…”

Section: Introductionmentioning

confidence: 99%

Fractional-order L_βC_αLow-Pass Filter Circuit

Zhou¹,

Zhang²,

Chen³

2015

Journal of Electrical Engineering and Technology

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-This paper introduces the fundamentals of the conventional LC low-pass filter circuit in the fractional domain. First, we study the new fundamentals of fractional-order LC low-pass filter circuit including the pure real angular frequency, the pure imaginary angular frequency and the short circuit angular frequency. Moreover, sensitivity analysis of the impedance characteristics and phase characteristics of the LC low-pass filter circuit with respect to the system variables is studied in detail, which shows the greater flexibility of the fractional-order filter circuit in designs. Furthermore, from the filtering property perspective, we systematically investigate the effects of the system variables (LC, frequency f and fractional orders) on the amplitude-frequency characteristics and phase-frequency characteristics. In addition, the detailed analyses of the cut-off frequency and filter factor are presented. Numerical experimental results are presented to verify the theoretical results introduced in this paper.

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“…Time delay is inevitable in modeling gene regulation processes. The discrete time delays have been considered in many researches . However, this may be too simple to express the movement of macromolecule.…”

Section: Introductionmentioning

confidence: 99%

“…In addition, the uncertainties such as external perturbations, parameter fluctuations, and data errors are inevitable by using approximate models. Moreover, it is easy to see that the linear fractional uncertainty can reduce to norm bounded one, which has been investigated in . Therefore, we should study the genetic regulatory networks with a structured linear fractional form uncertainties and stochastic disturbance.…”

Section: Introductionmentioning

confidence: 99%

“…In , the asymptotic stability analysis problem for genetic regulatory networks with interval time delays and norm‐bounded type uncertainties was presented. Besides, a model for delayed genetic regulatory networks with linear fractional uncertainties and stochastic perturbations is studied in . The study in investigates the delay‐probability‐distribution‐dependent stability problem of stochastic genetic regulatory networks with both discrete time delays and distributed time delays.…”

Section: Introductionmentioning

confidence: 99%

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Robust delay-probability-distribution-dependent stability of uncertain stochastic genetic regulatory networks with random discrete delays and distributed delays

Wang

Zhong

Liu

et al. 2013

Int. J. Robust. Nonlinear Control

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SUMMARYThis study is concerned with the problem of robust delay‐probability‐distribution‐dependent stability of uncertain stochastic genetic regulatory networks with mixed time‐varying delays. The parameter uncertainties are modeled as having a structured linear fractional form. Besides, we consider that the derivatives of the discrete time delays have different upper bounds in various delay intervals. Moreover, less conservative conditions are obtained by choosing an augmented novel Lyapunov–Krasovskii functional and using the lower bound lemma together with the Jensen inequality lemma. Furthermore, the criteria can be applicable to both fast and slow time‐varying delays. Finally, numerical examples are presented to illustrate the effectiveness of the theoretical results. Copyright © 2013 John Wiley & Sons, Ltd.

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Robust stability for genetic regulatory networks with linear fractional uncertainties

Cited by 31 publications

References 25 publications

Stability Analysis of Delayed Genetic Regulatory Networks via a Relaxed Double Integral Inequality

Stability Analysis of Delayed Genetic Regulatory Networks via a Relaxed Double Integral Inequality

Fractional-order L_βC_αLow-Pass Filter Circuit

Robust delay-probability-distribution-dependent stability of uncertain stochastic genetic regulatory networks with random discrete delays and distributed delays

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Robust stability for genetic regulatory networks with linear fractional uncertainties

Cited by 31 publications

References 25 publications

Stability Analysis of Delayed Genetic Regulatory Networks via a Relaxed Double Integral Inequality

Stability Analysis of Delayed Genetic Regulatory Networks via a Relaxed Double Integral Inequality

Fractional-order LβCαLow-Pass Filter Circuit

Robust delay-probability-distribution-dependent stability of uncertain stochastic genetic regulatory networks with random discrete delays and distributed delays

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Fractional-order L_βC_αLow-Pass Filter Circuit