Robust delay-probability-distribution-dependent stability of uncertain stochastic genetic regulatory networks with random discrete delays and distributed delays

Abstract

SUMMARYThis study is concerned with the problem of robust delay‐probability‐distribution‐dependent stability of uncertain stochastic genetic regulatory networks with mixed time‐varying delays. The parameter uncertainties are modeled as having a structured linear fractional form. Besides, we consider that the derivatives of the discrete time delays have different upper bounds in various delay intervals. Moreover, less conservative conditions are obtained by choosing an augmented novel Lyapunov–Krasovskii functional and using the lower bound lemma together with the Jensen inequality lemma. Furthermore, the criteria can be applicable to both fast and slow time‐varying delays. Finally, numerical examples are presented to illustrate the effectiveness of the theoretical results. Copyright © 2013 John Wiley & Sons, Ltd.

New delay-dependent stability criteria of genetic regulatory networks subject to time-varying delays

“…Therefore, it follows from the Lyapunov stability theory that the GRNs (6) with time-varying delays are globally asymptotically stable. Remark 2: It is worth noting that, motivated by [28], the triple integral terms t−σ2 y(s)ds, which is different compared with the results in [29], [30]. Remark 3: Note that the Jensen inequality as in [27] is commonly employed for time-delay systems to deal with the integral terms in the Lyapunov-Krasovskii functional.…”

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

“…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]). …”

Stability and bifurcation analysis of a gene expression model with small RNAs and mixed delays

“…Due to the complexity of the interaction of gene information in reality, the time delay of the system is not invariable [21][22][23], and it may produce complicated nonlinear phenomena with the change of time. According to literature [24][25][26][27][28], we find that there may be more than one kind of time delay in practical engineering systems.…”