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Wang J, Wang H, Shen H, Wang B, Park JH. Finite-Time H ∞ State Estimation for PDT-Switched Genetic Regulatory Networks With Randomly Occurring Uncertainties. IEEE/ACM TRANSACTIONS ON COMPUTATIONAL BIOLOGY AND BIOINFORMATICS 2022; 19:1651-1660. [PMID: 33242311 DOI: 10.1109/tcbb.2020.3040979] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/11/2023]
Abstract
This article is concerned with the problem of finite-time 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 article 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.
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New Results on Global Exponential Stability of Genetic Regulatory Networks with Diffusion Effect and Time-Varying Hybrid Delays. Neural Process Lett 2021. [DOI: 10.1007/s11063-021-10573-z] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/20/2022]
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Liu C, Wang X, Xue Y. Global exponential stability analysis of discrete-time genetic regulatory networks with time-varying discrete delays and unbounded distributed delays. Neurocomputing 2020. [DOI: 10.1016/j.neucom.2019.09.047] [Citation(s) in RCA: 22] [Impact Index Per Article: 5.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/01/2022]
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Jiao T, Zong G, Nguang SK, Zhang C. Stability Analysis of Genetic Regulatory Networks With General Random Disturbances. IEEE Trans Nanobioscience 2018; 18:128-135. [PMID: 30575542 DOI: 10.1109/tnb.2018.2887305] [Citation(s) in RCA: 30] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
Abstract
This paper establishes the stability criteria for genetic regulatory networks with random disturbances. We assume the nonlinear feedback regulation function to satisfy the sector-like condition and the random perturbation to have a finite second-order moment. First, under the globally Lipschitz condition, the existence and uniqueness of solution to random genetic regulatory networks are considered by exploiting an iterative approximation method. Then, by feat of the random analysis method and matrix technique, sufficient conditions are given to guarantee the noise-to-state stability in mean and globally asymptotic stability in probability, respectively. At last, two simulation examples are exploited in order to verify the validity of the proposed theory.
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Zhang X, Fan X, Wu L. Reduced- and Full-Order Observers for Delayed Genetic Regulatory Networks. IEEE TRANSACTIONS ON CYBERNETICS 2018; 48:1989-2000. [PMID: 28742049 DOI: 10.1109/tcyb.2017.2726015] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
This paper is centered upon the state estimation for delayed genetic regulatory networks. Our aim is at estimating the concentrations of mRNAs and proteins by designing reduced-order and full-order state observers based on available network outputs. We introduce a Lyapunov-Krasovskii functional including quadruplicate integrals, and estimate its derivative by employing the Wirtinger-type integral inequalities, reciprocal convex technique, and convex technique. From which, delay-dependent sufficient conditions, in the form of linear matrix inequalities (LMIs), are investigated to ensure that the resultant error system is asymptotically stable. One can verify these conditions by utilizing the MATLAB Toolboxes LMI or YALMIP. In addition, the gains of reduced-order and full-order observers are represented by the feasible solutions of the LMIs, and thereby, the concrete expressions of the desired reduced-order and full-order state observers are presented. Finally, the simulation results of a numerical example are demonstrated, which explains the validity of the proposed method.
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Yu T, Liu J, Zeng Y, Zhang X, Zeng Q, Wu L. Stability Analysis of Genetic Regulatory Networks With Switching Parameters and Time Delays. IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS 2018; 29:3047-3058. [PMID: 28678715 DOI: 10.1109/tnnls.2016.2636185] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
This paper is concerned with the exponential stability analysis of genetic regulatory networks (GRNs) with switching parameters and time delays. In this paper, a new integral inequality and an improved reciprocally convex combination inequality are considered. By using the average dwell time approach together with a novel Lyapunov-Krasovskii functional, we derived some conditions to ensure the switched GRNs with switching parameters and time delays are exponentially stable. Finally, we give two numerical examples to clarify that our derived results are effective.
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Zhang X, Han Y, Wu L, Wang Y. State Estimation for Delayed Genetic Regulatory Networks With Reaction-Diffusion Terms. IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS 2018; 29:299-309. [PMID: 28113959 DOI: 10.1109/tnnls.2016.2618899] [Citation(s) in RCA: 24] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
This paper addresses the problem of state estimation for delayed genetic regulatory networks (DGRNs) with reaction-diffusion terms using Dirichlet boundary conditions. The nonlinear regulation function of DGRNs is assumed to exhibit the Hill form. The aim of this paper is to design a state observer to estimate the concentrations of mRNAs and proteins via available measurement techniques. By introducing novel integral terms into the Lyapunov-Krasovskii functional and by employing the Wirtinger-type integral inequality, the convex approach, Green's identity, the reciprocally convex approach, and Wirtinger's inequality, an asymptotic stability criterion of the error system was established in terms of linear matrix inequalities (LMIs). The stability criterion depends upon the bounds of delays and their derivatives. It should be noted that if the set of LMIs is feasible, then the desired observation of DGRNs is possible, and the state estimation can be determined. Finally, two numerical examples are presented to illustrate the availability and applicability of the proposed scheme design.
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Song Y, Hu J, Chen D, Liu Y, Alsaadi FE, Sun G. A resilience approach to state estimation for discrete neural networks subject to multiple missing measurements and mixed time-delays. Neurocomputing 2018. [DOI: 10.1016/j.neucom.2017.06.065] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/19/2022]
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Ali MS, Gunasekaran N, Ahn CK, Shi P. Sampled-Data Stabilization for Fuzzy Genetic Regulatory Networks with Leakage Delays. IEEE/ACM TRANSACTIONS ON COMPUTATIONAL BIOLOGY AND BIOINFORMATICS 2018; 15:271-285. [PMID: 28113380 DOI: 10.1109/tcbb.2016.2606477] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
This paper deals with the sampled-data stabilization problem for Takagi-Sugeno (T-S) fuzzy genetic regulatory networks with leakage delays. A novel Lyapunov-Krasovskii functional (LKF) is established by the non-uniform division of the delay intervals with triplex and quadruplex integral terms. Using such LKFs for constant and time-varying delay cases, new stability conditions are obtained in the T-S fuzzy framework. Based on this, a new condition for the sampled-data controller design is proposed using a linear matrix inequality representation. A numerical result is provided to show the effectiveness and potential of the developed design method.
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Zou C, Wei X, Zhang Q, Zhou C. Passivity of Reaction–Diffusion Genetic Regulatory Networks with Time-Varying Delays. Neural Process Lett 2017. [DOI: 10.1007/s11063-017-9682-7] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
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Fan X, Zhang X, Wu L, Shi M. Finite-Time Stability Analysis of Reaction-Diffusion Genetic Regulatory Networks with Time-Varying Delays. IEEE/ACM TRANSACTIONS ON COMPUTATIONAL BIOLOGY AND BIOINFORMATICS 2017; 14:868-879. [PMID: 27093707 DOI: 10.1109/tcbb.2016.2552519] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/05/2023]
Abstract
This paper is concerned with the finite-time stability problem of the delayed genetic regulatory networks (GRNs) with reaction-diffusion terms under Dirichlet boundary conditions. By constructing a Lyapunov-Krasovskii functional including quad-slope integrations, we establish delay-dependent finite-time stability criteria by employing the Wirtinger-type integral inequality, Gronwall inequality, convex technique, and reciprocally convex technique. In addition, the obtained criteria are also reaction-diffusion-dependent. Finally, a numerical example is provided to illustrate the effectiveness of the theoretical results.
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Ling G, Guan ZH, Hu B, Lai Q, Wu Y. Multistability and Bifurcation Analysis of Inhibitory Coupled Cyclic Genetic Regulatory Networks With Delays. IEEE Trans Nanobioscience 2017; 16:216-225. [PMID: 28212091 DOI: 10.1109/tnb.2017.2669112] [Citation(s) in RCA: 23] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/06/2022]
Abstract
Many biological systems have the conspicuous property to present more than one stable state and diverse rhythmic behaviors. A closed relationship between these complex dynamic behaviors and cyclic genetic structures has been witnessed by pioneering works. In this paper, a typical structure of inhibitory coupled cyclic genetic networks is introduced to further enlighten this mechanism of stability and biological rhythms of living cells. The coupled networks consist of two identical cyclic genetic subnetworks, which inhibit each other directly. Each subnetwork can be regarded as a genetic unit at the cellular level. Multiple time delays, including both internal and coupling delays, are considered. The existence of positive equilibriums for this kind of coupled systems is proved, and the stability for each equilibrium is analyzed without or with delays. It is shown that the coupled networks with positive cyclic genetic units have an ability to show multistability, while the coupled networks with negative units may present a series of Hopf bifurcations with the variation of time delays. Several numerical simulations are made to prove our results.
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Wang X, Yang GH. Distributed fault-tolerant control for a class of cooperative uncertain systems with actuator failures and switching topologies. Inf Sci (N Y) 2016. [DOI: 10.1016/j.ins.2015.11.002] [Citation(s) in RCA: 43] [Impact Index Per Article: 5.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
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Prieto A, Prieto B, Ortigosa EM, Ros E, Pelayo F, Ortega J, Rojas I. Neural networks: An overview of early research, current frameworks and new challenges. Neurocomputing 2016. [DOI: 10.1016/j.neucom.2016.06.014] [Citation(s) in RCA: 161] [Impact Index Per Article: 20.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/24/2023]
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Li Z, Chen D, Liu Y, Zhao Y. New delay-dependent stability criteria of genetic regulatory networks subject to time-varying delays. Neurocomputing 2016. [DOI: 10.1016/j.neucom.2016.05.066] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/21/2022]
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Zhang X, Han Y, Wu L, Zou J. M-matrix-based globally asymptotic stability criteria for genetic regulatory networks with time-varying discrete and unbounded distributed delays. Neurocomputing 2016. [DOI: 10.1016/j.neucom.2015.10.024] [Citation(s) in RCA: 17] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/22/2022]
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