Stochastic stability of Markovian jumping uncertain stochastic genetic regulatory networks with interval time-varying delays. (English) Zbl 1194.92030

Summary: This paper investigates the robust stability problem of stochastic genetic regulatory networks with interval time-varying delays and Markovian jumping parameters. The structure variations at discrete time instances during the process of gene regulations, known as hybrid genetic regulatory networks based on Markov processes, are proposed. The jumping parameters considered are generated from a continuous-time discrete-state homogeneous Markov process, which is governed by a Markov process with discrete and finite state space. A new type of Markovian jumping matrices \(P_i\) and \(Q_i\) is introduced in this paper. The parameter uncertainties are assumed to be norm bounded and the discrete delay is assumed to be time-varying and belong to a given interval, which means that the lower and upper bounds of interval time-varying delays are unavoidable. Based on the Lyapunov-Krasovskii functional and stochastic stability theory, delay-interval dependent stability criteria are obtained in terms of linear matrix inequalities. Some numerical examples are given to illustrate the effectiveness of our theoretical results.


92C42 Systems biology, networks
60J20 Applications of Markov chains and discrete-time Markov processes on general state spaces (social mobility, learning theory, industrial processes, etc.)
15A45 Miscellaneous inequalities involving matrices
60J25 Continuous-time Markov processes on general state spaces
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