Stochastic stability for delayed semi-Markovian genetic regulatory networks with partly unknown transition rates by employing new integral inequalities.

This paper discusses the stochastic stability for genetic regulatory networks (GRNs) with semi-Markov switching and time-varying delays where the transition rates (TRs) of the modes are partially unknown. By proposing vectors with three Legendre polynomials and three weighted Legendre polynomials, two free-matrix-based integral inequalities are derived, which involves several existing ones as their special cases. Then, two appropriate Lyapunov–Krasovskii functionals (LKFs) are established to be apt for the acquired inequalities. By introducing some free-weight matrices and utilizing the acquired integral inequalities, new sufficient conditions are proposed to ensure the stochastically asymptotic stability of analyzed networks in the mean-square sense. Finally, two simulation examples are put forward to show the effectiveness and less conservatism of the presented criteria. [ABSTRACT FROM AUTHOR]