M-matrix-based delay-range-dependent global asymptotical stability criterion for genetic regulatory networks with time-varying delays

This paper is concerned with the problem of global asymptotical stability for a class of delayed genetic regularity networks (GRNs), where the time delays belong to given intervals and assumed to be time-varying. By choosing an appropriate and novel Lyapunov functional and utilizing M-matrix theory, we derive an M-matrix-based delay-range-dependent sufficient condition under which the class of considered GRNs has unique nonnegative equilibrium point which is globally asymptotically stable. The sufficient condition given here is to check whether a constructed constant matrix is a nonsingular M-matrix. This can be easily done, since there are more than 50 equivalent conditions of nonsingular M-matrix, and hence the stability criterion obtained in this paper is different from existing ones in the form of linear matrix inequality (LMI). Finally, several examples and their simulations are presented to show the effectiveness of the proposed approach.