Abstract
In this paper, we present some novel results for robust passivity of a class of uncertain discrete-time Markovian jumping genetic regulatory networks (GRNs) with time-varying delays. By constructing a new set of Lyapunov–Krasovskii functionals, together with the matrix inequality technique, we provide a new set of results for the passiveness, and also ensure the mean-square asymptotical stability (internally) of the considered GRNs about their equilibrium points for all time delays satisfying both the lower bound and upper bound of the interval time-varying delay. Further, the obtained results are extended to deal with the robust passiveness of the considered GRNs for all admissible uncertainties. The obtained conditions are derived in terms of linear matrix inequalities (LMIs), which can be easily verified via the LMI toolbox. Finally, numerical examples with simulation results are provided for the GRN model to illustrate the applicability and usefulness of the theory.
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