Global exponential stability analysis of discrete-time genetic regulatory networks with time-varying discrete delays and unbounded distributed delays

Liu, Chunyan; Wang, Xin; Xue, Yuncan

doi:10.1016/j.neucom.2019.09.047

Cited by 32 publications

(25 citation statements)

References 47 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Assume H1 holds, then system (1) is globally exponentially stable if the following two inequalities hold x2(2, t) Remark 2. The model of RDGRNs with discrete and distributed delays is general compared with the models in [30]- [37], [43]- [51]. The models in [30]- [37] are restricted to be delayed ordinary differential equations.…”

Section: Resultsmentioning

confidence: 99%

“…The model of RDGRNs with discrete and distributed delays is general compared with the models in [30]- [37], [43]- [51]. The models in [30]- [37] are restricted to be delayed ordinary differential equations. Since the model in this paper can be viewed as a special case of delayed partial differential equations in light of effect of the reaction diffusion, it shows superiority in the case of nonuniform space.…”

Section: Resultsmentioning

confidence: 99%

“…Considering the discrete and distributed delays, authors in [30]- [35] studied the stability for delayed GRNs. Further, the global asymptotic and exponential stability of GRNs with discrete and infinite distributed delays was analyzed in [36], [37]. When the infinite distributed delays are involved, the global exponential stability problem of GRNs with mixed time delays is a difficult task, which deserves further investigation.…”

Section: Introductionmentioning

confidence: 99%

“…1) The discrete delays, infinite distributed delays and reaction diffusion are all considered in constructing the general and accurate model of GRNs, which makes the model more generalized compared to GRNs with distributed delays in [30]- [37], and RDGRNs without distributed delays in [43]- [51].…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Algebraic Stability Criteria of Reaction Diffusion Genetic Regulatory Networks With Discrete and Distributed Delays

et al. 2021

View full text Add to dashboard Cite

This paper addresses the stability problem of genetic regulatory networks by involving the spatial diffusion of concentration, discrete and infinite distributed delays. By using the theories of partial differential equation and Lyapunov stability, the global exponential stability criteria in algebraic form are derived for reaction diffusion genetic regulatory networks (RDGRNs) with discrete and distributed delays. The derived stability conditions are simple and can be directly calculated by using the parameters of the networks. Moreover, the theoretical results are universal and can be applied to deal with the stability problem of RDGRNs with or without distributed delays. Eventually, the validity and feasibility of the results are illustrated by numerical simulations. INDEX TERMS Global exponential stability, reaction diffusion, genetic regulatory networks, infinite distributed delays.

show abstract

Section: Resultsmentioning

confidence: 99%

Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Algebraic Stability Criteria of Reaction Diffusion Genetic Regulatory Networks With Discrete and Distributed Delays

et al. 2021

View full text Add to dashboard Cite

show abstract

“…Here are a few examples to illustrate the research status of GRNs in recent years. In [11], the problem of exponential stability of GRNs was studied, and time-varying discrete delays and unbounded distributed delays were also considered. Based on round-robin protocols, the state estimation problem of GRNs with stochastic process noises and bounded exogenous disturbances was analyzed in [12].…”

Section: Introductionmentioning

confidence: 99%

Finite-Time $\mathcal{H}_{\infty }$ State Estimation for PDT-Switched Genetic Regulatory Networks with Randomly Occurring Uncertainties

Wang

Shen

et al. 2020

IEEE/ACM Trans. Comput. Biol. and Bioinf.

View full text Add to dashboard Cite

This paper is concerned with the problem of finitetime H∞ state estimation for switched genetic regulatory networks with randomly occurring uncertainties. The persistent dwell-time switching rule, as a more versatile class of switching rules, is considered in this paper. Besides, several random variables that obey the Bernoulli distribution are used to represent randomly occurring uncertainties. The overriding purpose of this paper is to design an estimator to ensure that the estimation error system is stochastically finite-time bounded and satisfies the H∞ performance. Based on this, sufficient conditions for the explicit form of the estimator gains can be obtained by the Lyapunov method. Finally, a numerical example is given to verify the correctness and feasibility of the proposed method. Index Terms-Switched genetic regulatory networks, finitetime H∞ state estimation, persistent dwell-time switching rule, randomly occurring uncertainties.

show abstract

State observer for delayed gene regulatory networks with coupled cyclic‐central structure

Zhang

Yan

Wang

et al. 2022

Adaptive Control & Signal

Self Cite

View full text Add to dashboard Cite

This article researches the state observer for delayed gene regulatory networks (GRNs) with coupled cyclic-central structure. The GRN under consideration consists of a cyclic subnet and a central subnet, which have multiple directed promotions or inhibitions. The goal is to estimate the states of the considered GRNs through the known measurement output. A sufficient condition for the global exponential stability of the error system is obtained by the definitions of the global exponential stability and the Moore-Penrose inverse of matrix. Thereby, a desired state observer of the studied GRNs is given. Lastly, a numerical example is presented to verify the validity of the designed state observer.

show abstract

Global exponential stability analysis of discrete-time genetic regulatory networks with time-varying discrete delays and unbounded distributed delays

Cited by 32 publications

References 47 publications

Algebraic Stability Criteria of Reaction Diffusion Genetic Regulatory Networks With Discrete and Distributed Delays

Algebraic Stability Criteria of Reaction Diffusion Genetic Regulatory Networks With Discrete and Distributed Delays

Finite-Time $\mathcal{H}_{\infty }$ State Estimation for PDT-Switched Genetic Regulatory Networks with Randomly Occurring Uncertainties

State observer for delayed gene regulatory networks with coupled cyclic‐central structure

Contact Info

Product

Resources

About