Robust stability analysis of Markov jump standard genetic regulatory networks with mixed time delays and uncertainties

This paper concerns the robust stability analysis problems for a class of nonlinear Markov jump standard genetic regulatory networks with mixed time-varying delays and parameter uncertainties. The standard genetic regulatory networks model is constructed via recurrent neural networks. The nonlinear regulatory function is assumed to satisfy the sector condition, and each regulatory function in the model has its own expression form. The mixed delays mean that the discrete delays and distributed delays are considered simultaneously. Based on linear matrix inequality techniques, sufficient conditions for robust stability of the underlying systems are first derived by using the conventional approach in the area of time-delay systems. Also, the "delay decomposition" approach is further utilized so as to improve the analytical results. Two numerical examples are exploited to verify the obtained theoretical findings. Crown Copyright (C) 2013 Published by Elsevier B.V. All rights reserved.