Finite-time H∞ control for discrete-time genetic regulatory networks with random delays and partly unknown transition probabilities

The finite-time H∞ control problem is investigated in this paper for a class of discrete-time genetic regulatory networks (GRNs) with random delays. The time-delay is modeled as a Markov chain and the transition probabilities of the jumping process are assumed to be partly unknown transition probabilities. By using a properly constructed Lyapunov function, a sufficient condition is obtained in terms of linear matrix inequalities (LMIs), which can guarantee the finite-time stochastic stability, boundedness of the GRN. Then, an optimization problem with LMIs constraints is established to design a finite-time H∞ controller which ensures H∞ disturbance attenuation level. Finally, two illustrative examples are given to demonstrate the effectiveness of the proposed results.