Toward non-conservative stability conditions for equilibrium points of genetic networks with SUM regulatory functions

An important problem in systems biology consists of establishing whether an equilibrium point of a genetic regulatory network is stable. This paper investigates this problem for genetic networks with SUM regulatory functions. It is shown that a sufficient condition for global asymptotical stability of an equilibrium point of these networks can be derived in terms of convex optimizations with LMI constraints by exploiting polynomial Lyapunov functions and SOS techniques. This condition is interesting because does not introduce approximations of the nonlinearities present in the genetic regulatory network, and the conservatism can be decreased by increasing the degree of the involved polynomials.