Robust stability of impulsive genetic regulatory networks with time-varying delays

The purpose of this paper is to investigate a new robust stability criterion of impulsive genetic regulatory networks with time-varying delays based on Lyapunov functional. The SUM logic which describes transcription factor is utilized to model the genetic regulatory mechanism. For the impulsive genetic regulatory networks with time-varying delays, both continuous and discontinuous time interval will be discussed separately. Lyapunov based sufficient conditions for the asymptotic stability of impulsive genetic regulatory networks are obtained by adopting 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 illustrate the effectiveness of the developed results.