H∞Filtering for Discrete-Time Genetic Regulatory Networks with Random Delay Described by a Markovian Chain

Abstract

This paper is concerned with theH∞filtering problem for a class of discretetime genetic regulatory networks with random delay and external disturbance. The aim is to designH∞filter to estimate the true concentrations of mRNAs and proteins based on available measurement data. By introducing an appropriate Lyapunov function, a sufficient condition is derived in terms of linear matrix inequalities (LMIs) which makes the filtering error system stochastically stable with a prescribedH∞disturbance attenuation level. The filter gains are given by solving the LMIs. Finally, an illustrative example is given to demonstrate the effectiveness of the proposed approach; that is, our approach is available for a smallerH∞disturbance attenuation level than one in (Liu et al., 2012).

Asymptotic Stability Criteria for Genetic Regulatory Networks with Time-Varying Delays and Reaction–Diffusion Terms

“…Moreover, we can get the corresponding observer gain matrices as follows: K 1 = P −1 1 W 1 = 0, K 2 = P −1 2 W 2 = 1.5571. Further, when σ(t) = τ (t) = 1, the state responses of GRN (37), observer (5) and the corresponding error system are given in Figures 1-6. V. CONCLUSIONS In this paper, the state estimation problem for a class of GRNs with time-varying delays and reaction-diffusion terms are studied.…”

“…A great amount of experimental results show that mathematical modeling of GRNs can be a powerful tool for researching the gene regulation process and discovering complex structure of a biological organism [1]- [3]. Generally, there are two basic models for GRNs: Boolean model (discrete-time model) [4], [5] and differential equation model (continuous-time model) [6]- [8]. Differential equation model describes the change rates of the concentrations of mRNAs and proteins.…”

“…In order to understand biological networks better, it is indispensable to estimate the states of the nodes through available measurements. Hence, the problem of state estimation for biological networks has been one of the investigated dynamical behaviors in recent years [5], [29]- [33]. However, to the best of the authors' knowledge, there is still no any published result on the state estimation problem for GRNs with time-varying delays and reaction-diffusion terms, which arouses our research interests.…”

An Improved Integral Inequality to Stability Analysis of Genetic Regulatory Networks With Interval Time-Varying Delays

“…Mathematical modeling of GRNs as dynamical system models provides a powerful tool for studying gene regulation processes in living organisms, models of GRNs in literature can be roughly classified into two types, i.e., the discrete model [1], [2], [26] and the continuous model [3], [4], [5], [6]. Usually, a continuous model is described by a (functional) differential equation.…”

“…It has been well recognized that time delay is one of the main sources leading to instability and poor performance of a system [7], [8], [9]. As a result, much effort has been paid to the study of GRNs described by FDEMs, and many significant results have been reported in literature on the stability analysis, controller synthesis, filter design, and so on (see, e.g., [7], [8], [10], [11], [12], [13], [14], [15], [16], [17], [18], [19], [20], [21], [22], [23], [24], [25], [26], [27], [28]). …”