Stability Analysis for Markov-type Genetic Regulatory Network with Time Delays and Partial Information on Transition Probabilities

To address the stability problem in Markov-type genetic regulatory networks (GRNs) that contain only partial information on transition probabilities and time delays, we propose GRN delay-dependent stability criteria. We develop an augmented Lyapunov function that includes time delay information for the process of transcription and translation. By weakening the conditions of the augmented Lyapunov function, we use the extended Wirtinger's inequality to estimate the weak infinitesimal operator of the Lyapunov-Krasovskii function (LKF). Finally, numerical examples and simulations are provided to illustrate the proposed method's effectiveness and merits.