Robust stability of stochastic delayed genetic regulatory networks

In this paper, a new robust stability analysis for stochastic genetic regulatory networks with interval parameters based on Lyapunov functional and stochastic differential equation theory is researched. The SUM logic which describes transcription factor is used to model the genetic regulatory mechanism. Markov chain is considered state switching mechanism as hybrid systems. Lyapunov based sufficient conditions for the asymptotic stability of stochastic genetic regulatory networks are obtained by employing bounding techniques and free-weighting matrices. Schur complements will be applied to express all the derived stability conditions in terms of LMIs. The new criterion is applicable to both fast and slow time-varying delay cases. Finally, a numerical example is presented to demonstrate the effectiveness of the developed results.