Robust stability for uncertain genetic regulatory networks with interval time-varying delays

This paper addresses the problem of robust stability of uncertain genetic regulatory networks (GRNs) with interval time-varying delays. We derive some new delay-range-dependent and delay-derivative-dependent/independent stability criteria by employing some free-weighting matrices and linear matrix inequalities. In our analysis, we carefully consider the relationship between the time-varying state delays and their bounds when calculating the upper bound of the derivative of Lyapunov functional. We hence show that, the rigorous requirement of other literatures that the time-derivatives of time-varying delays must be smaller than one is abandoned in the proposed scheme. The new criteria are applicable to both fast and slow time-varying delays. Finally, four numerical examples are presented to illustrate the effectiveness and the less conservativeness of the developed results. (C) 2010 Elsevier Inc. All rights reserved.