Control of genetic regulatory networks with partially unknown transition probabilities

A problem of state feedback stochastic stability and stabilization of a class of genetic regulatory networks (GRNs) with both intrinsic and extrinsic stochastic perturbations (noise) are investigated under Markovian switching. The non-linear regulatory function is assumed to satisfy a sector-like condition and the jump Markovian switching is modeled by a discrete-time Markov chain with partial information on transition probability matrix. We proposed a stability criterion by utilizing Lyapunov second method, an improved-free weighting matrix method and the Lur´e system approach with partially unknown or completely unknown transition probability matrix. Sufficient conditions for stability and state feedback stabilization are obtained and represented by linear matrix inequalities (LMIs), which can be numerically solved by LMI tool box and CVX package in MATLAB. Two numerical example are given to demonstrate the merits of the obtained results.