Delay partition method for the robust stability of uncertain genetic regulatory networks with time-varying delays

The robust stability analysis for genetic regulatory networks with parameter uncertainties and time-varying delays is investigated in this study. Firstly, some new variables are defined to deal with the uncertain parameters. Then, we improve the Lyapunov-Krasovskii functional by partitioning the interval time-varying delays into non-uniformly subintervals and decomposing integral intervals accordingly. In this way, the bounds of time delays can be estimated more accurately. Besides, two modulus have been introduced in the delay derivative terms to obtain better delay-derivation-dependent stability criteria. Furthermore, we have employed Jensen׳s inequality together with convex combination method to handle integral terms to render less conservative conditions. Finally, the stability criteria turn out to be feasible and effective via numerical examples.