Investigating stochastic stability of uncertain genetic networks via LMIs

This paper addresses the problem of investigating stochastic stability of uncertain genetic networks with SUM regulatory functions. Specifically, the genetic network is assumed to be affected by Wiener processes, and its coefficients are parametrized by an unknown vector constrained in a hypercube. By using the square matricial representation (SMR) of matrix polynomials, it is shown that a condition for stochastic stability of the uncertain genetic network with disturbance attenuation guaranteed for all admissible values of the parameter can be derived in terms of linear matrix inequalities (LMIs). Some examples illustrate the proposed condition.