Approximation of state variables for discrete-time stochastic genetic regulatory networks with leakage, distributed, and probabilistic measurement delays: a robust stability problem.
| Title: | Approximation of state variables for discrete-time stochastic genetic regulatory networks with leakage, distributed, and probabilistic measurement delays: a robust stability problem. |
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| Authors: | Pandiselvi S; 1Department of Mathematics, Alagappa University, Karaikudi, India.; Raja R; 2Ramanujan Centre for Higher Mathematics, Alagappa University, Karaikudi, India.; Cao J; 3School of Mathematics, Southeast University, Nanjing, China.; Rajchakit G; 4Department of Mathematics, Faculty of Science, Maejo University, Chiang Mai, Thailand.; Ahmad B; 5Nonlinear Analysis and Applied Mathematics (NAAM) Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah, Saudi Arabia. |
| Source: | Advances in difference equations [Adv Differ Equ] 2018; Vol. 2018 (1), pp. 123. Date of Electronic Publication: 2018 Apr 03. |
| Publication Type: | Journal Article |
| Language: | English |
| Journal Info: | Publisher: SpringerOpen Country of Publication: Germany NLM ID: 101670234 Publication Model: Print-Electronic Cited Medium: Print ISSN: 1687-1839 (Print) Linking ISSN: 16871839 NLM ISO Abbreviation: Adv Differ Equ Subsets: PubMed not MEDLINE |
| Imprint Name(s): | Publication: 2012- : Heidelberg : SpringerOpen; Original Publication: Cairo : Hindawi Publishing Corporation, 2004- |
| Abstract: | This work predominantly labels the problem of approximation of state variables for discrete-time stochastic genetic regulatory networks with leakage, distributed, and probabilistic measurement delays. Here we design a linear estimator in such a way that the absorption of mRNA and protein can be approximated via known measurement outputs. By utilizing a Lyapunov-Krasovskii functional and some stochastic analysis execution, we obtain the stability formula of the estimation error systems in the structure of linear matrix inequalities under which the estimation error dynamics is robustly exponentially stable. Further, the obtained conditions (in the form of LMIs) can be effortlessly solved by some available software packages. Moreover, the specific expression of the desired estimator is also shown in the main section. Finally, two mathematical illustrative examples are accorded to show the advantage of the proposed conceptual results. |
| Competing Interests: | The authors declare that they have no competing interests. |
| References: | IEEE Trans Neural Netw. 2008 Mar;19(3):520-3. (PMID: 18334369); Math Biosci. 2008 Sep;215(1):55-63. (PMID: 18585740); Math Biosci. 2016 Aug;278:94-9. (PMID: 27326659); IEEE Trans Cybern. 2016 Dec;46(12 ):3377-3387. (PMID: 28055932) |
| Contributed Indexing: | Keywords: Distributed delays; Genetic regulatory networks (GRNs); Leakage delays; Probabilistic measurement delays; Time-varying delays |
| Entry Date(s): | Date Created: 20180410 Latest Revision: 20200929 |
| Update Code: | 20260130 |
| PubMed Central ID: | PMC5882887 |
| DOI: | 10.1186/s13662-018-1569-z |
| PMID: | 29628952 |
| Database: | MEDLINE |
Journal Article