Abstract
We deal with the design problem of nonfragile state estimator for discrete-time genetic regulatory networks (GRNs) with time-varying 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 Lyapunov-Krasovskii 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.
Highlights
Genetic regulatory networks (GRNs), which are biochemically dynamical systems describing highly complicated interactions among DNA, RNA, protein, and metabolic product in the interactive transcriptional and translational processes, have become an attractive research field in the systems biology and biomedical sciences during the past few decades
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 linear matrix inequalities (LMIs)
A great deal of effort has been made to deal with the analysis problem of GRNs with time-varying delays as well as stochastic noises and a growing number of approaches have been provided in the literature to examine the dynamical behaviors of the addressed GRNs [2, 3, 13]
Summary
Genetic regulatory networks (GRNs), which are biochemically dynamical systems describing highly complicated interactions among DNA, RNA, protein, and metabolic product in the interactive transcriptional and translational processes, have become an attractive research field in the systems biology and biomedical sciences during the past few decades. In the past few years, a great deal of attention has been devoted to the theoretical analysis and experimental investigation on GRNs. a large amount of important results has been reported in literature making significant contributions for understanding both static and dynamic behaviors of biological systems in detail (see [1,2,3] and the references therein). A great deal of effort has been made to deal with the analysis problem of GRNs with time-varying delays as well as stochastic noises and a growing number of approaches have been provided in the literature to examine the dynamical behaviors of the addressed GRNs [2, 3, 13]. The asymptotic stability problems have been investigated in [17,18,19] for discrete-time uncertain GRNs with time-varying delays and stochastic fluctuations, where some sufficient conditions have been presented to ensure the stability of the addressed GRNs via the linear matrix inequality approach
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