Robust asymptotic stability of fuzzy Markovian jumping genetic regulatory networks with time-varying delays by delay decomposition approach

Non-uniform sampled-data control for stochastic passivity and passification of Markov jump genetic regulatory networks with time-varying delays

“…The study of Markov jump GRNs has received much attention due to their theoretical importance and potential applications. It is worth mentioning that most of the researches mainly focus on the stability problem or the state estimation problem of GRNs and have achieved remarkable results [6,12,32,33]. In this paper, we investigate the non-uniform sampled-data control scheme to solve the passivity and passification problems of Markov jump GRNs.…”

Stability of genetic regulatory networks with time-varying delay: Delta operator method

“…In addition, due to the slow processes of gene transcription, diffusion, translation or the finite switching speed of amplifiers, time delays should be taken into account in GRNs. Many worthy results for GNRs with time delays have been reported in the literatures [1,2,[17][18][19]24,33]. To mention a few, the problem of stability for GRNs with time-varying delay has been also investigated.…”

Stability Analysis of Delayed Genetic Regulatory Networks via a Relaxed Double Integral Inequality

“…However, local stability is not enough for understanding nonlinear GRNs; the globally asymptotical stability of GRNs with SUM regulatory functions has been widely investigated [17][18][19][20][21][22]. Meanwhile, by taking into account the unavoidable uncertainties caused by modelling errors and parameter fluctuations, many scholars paid attentions to the robust stability analysis of the delayed GRNs [23][24][25][26][27][28][29][30][31][32][33][34][35][36]. Moreover, both the intrinsic noise derived from the random births and deaths of individual molecules and the extrinsic noise due to environment fluctuations make the gene regulation process 2 Mathematical Problems in Engineering an intrinsically noisy process [59].…”

“…The first one is the delay-partition-based LKFs, which is constructed by dividing the delay interval into several small subintervals and then replacing the original integral terms with multiple new integral terms based on delay subintervals. This type of LKF has been used to investigate the robust stability of various GRNs [25,26,51], the exponential stability of switch GRNs [56], and the stochastic stability of jumping GRNs [27,43,45]. The other is the augmented LKF constructed by using various state vectors (current and delayed and/or integrated state vectors, etc.)…”