Stochastic analysis and control of real-time systems with random time delays
Automatica (Journal of IFAC)
Stability of Time-Delay Systems
Stability of Time-Delay Systems
Brief paper: On the V-stability of complex dynamical networks
Automatica (Journal of IFAC)
Exponential Stability of Discrete-Time Genetic Regulatory Networks With Delays
IEEE Transactions on Neural Networks
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This paper on global exponential stability in the mean square sense of genetic regulatory networks (GRNs) is motivated by a practical consideration that different genes have different time delays for transcription and translation, and in some cases, each multimer is assigned to a randomly chosen gene promoter site as an activator or inhibitor. One important feature of the obtained results reported here is that the time-varying delays are assumed to be random and their probability distributions are known a priori. By employing the information of the probability distributions of the time delays, we present some stability criteria for the uncertain delayed genetic networks with SUM regulatory logic where each transcription factor acts additively to regulate a gene. The effects of both variation range and distribution probability of the time delays are taken into account in the proposed approach. Another feature of the results is that a novel Lyapunov functional dependence on auxiliary delay parameters is exploited, which renders the results to be potentially less conservative and allows the time-varying delays to be not differentiable. The theoretical findings are illustrated and verified with two examples.