Design of state estimator for genetic regulatory networks with time-varying delays and randomly occurring uncertainties

Sampled-Data Stabilization for Fuzzy Genetic Regulatory Networks with Leakage Delays

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.

GeRNet: a gene regulatory network tool

Gene regulatory networks (GRNs) are crucial in every process of life since they govern the majority of the molecular processes. Therefore, the task of assembling these networks is highly important. In particular, the so called model-free approaches have an advantage modeling the complexities of dynamic molecular networks, since most of the gene networks are hard to be mapped with accuracy by any other mathematical model. A highly abstract model-free approach, called rule-based approach, offers several advantages performing data-driven analysis; such as the requirement of the least amount of data. They also have an important ability to perform inferences: its simplicity allows the inference of large size models with a higher speed of analysis. However, regarding these techniques, the reconstruction of the relational structure of the network is partial, hence incomplete, for an effective biological analysis. This situation motivated us to explore the possibility of hybridizing with other approaches, such as biclustering techniques. This led to incorporate a biclustering tool that finds new relations between the nodes of the GRN. In this work we present a new software, called GeRNeT that integrates the algorithms of GRNCOP2 and BiHEA along a set of tools for interactive visualization, statistical analysis and ontological enrichment of the resulting GRNs. In this regard, results associated with Alzheimer disease datasets are presented that show the usefulness of integrating both bioinformatics tools.

Stability of genetic regulatory networks based on switched systems and mixed time-delays

In this paper, the switched genetic regulatory networks (GRNs) are modeled from a real biological system, based on switched systems, noise and mixed time-delays. Global asymptotical stability for the proposed switched GRNs are studied by the Lyapunov method and the matrix inequality techniques. Some new sufficient conditions are obtained to ensure the global asymptotical stability of the proposed switched GRNs. Furthermore, the proposed LMI results are computationally efficient as it can be solved numerically with standard commercial software. Finally, an example is provided to illustrate the usefulness of the results.

Exponential state estimation of Markovian jumping genetic regulatory networks with mode-dependent probabilistic time-varying delays

In this paper, we investigate a problem of exponential state estimation for Markovian jumping genetic regulatory networks with mode-dependent probabilistic time-varying delays. A new type of mode-dependent probabilistic leakage time-varying delay is considered. Given the probability distribution of the time-delays, stochastic variables that satisfying Bernoulli random binary distribution are formulated to produce a new system which includes the information of the probability distribution. Under these circumstances, the state estimator is designed to estimate the true concentration of the mRNA and the protein of the GRNs. Based on Lyapunov-Krasovskii functional that includes new triple integral terms and decomposed integral intervals, delay-distribution-dependent exponential stability criteria are obtained in terms of linear matrix inequalities. Finally, a numerical example is provided to show the usefulness and effectiveness of the obtained results.