Parameter-dependent linear matrix inequality approach to robust state estimation of noisy genetic networks

Abstract Genetic networks play an important role in systems biology as they explain the interactions between genes and proteins. However, the genetic networks are described by dynamical systems with nonlinear uncertainties and usually affected by stochastic internal fluctuations, and stochastic external disturbances. The design addressed in this paper is concerned with robust state estimator of stochastic genetic networks in the presence of nonlinear uncertainties. The objective is to estimate the true concentrations of mRNAs and proteins of the noisy nonlinear genetic networks. Based on the notion of Lyapunov functions, we improve the design condition for the robust estimator to ensure that the estimation error satisfies H∞ performance criterion. The sufficient condition is derived in terms of parameter-dependent linear matrix inequalities, which are convex constraints, and can be efficiently solved via the sum-of-squares technique. We provide two numerical examples of real genetic networks to illustrate the effectiveness of the proposed method.