Wang Z, Gao H, Cao J, Liu X
Department of Information Systems and Computing, Brunel University, Uxbridge, Middlesex, UK.
IEEE Trans Nanobioscience. 2008 Jun;7(2):154-63. doi: 10.1109/TNB.2008.2000746.
In this paper, we investigate the robust asymptotic stability problem of genetic regulatory networks with time-varying delays and polytopic parameter uncertainties. Both cases of differentiable and nondifferentiable time-delays are considered, and the convex polytopic description is utilized to characterize the genetic network model uncertainties. By using a Lyapunov functional approach and linear matrix inequality (LMI) techniques, the stability criteria for the uncertain delayed genetic networks are established in the form of LMIs, which can be readily verified by using standard numerical software. An important feature of the results reported here is that all the stability conditions are dependent on the upper and lower bounds of the delays, which is made possible by using up-to-date techniques for achieving delay dependence. Another feature of the results lies in that a novel Lyapunov functional dependent on the uncertain parameters is utilized, which renders the results to be potentially less conservative than those obtained via a fixed Lyapunov functional for the entire uncertainty domain. A genetic network example is employed to illustrate the applicability and usefulness of the developed theoretical results.
在本文中，我们研究了具有时变延迟和多面体参数不确定性的基因调控网络的鲁棒渐近稳定性问题。考虑了可微和不可微时滞两种情况，并利用凸多面体描述来刻画基因网络模型的不确定性。通过使用Lyapunov泛函方法和线性矩阵不等式（LMI）技术，以LMI的形式建立了不确定延迟基因网络的稳定性准则，可使用标准数值软件轻松验证。这里报告的结果的一个重要特征是，所有稳定性条件都依赖于延迟的上下界，这是通过使用实现延迟依赖性的最新技术得以实现的。结果的另一个特征在于，使用了一种依赖于不确定参数的新型Lyapunov泛函，这使得结果可能比在整个不确定性域中通过固定Lyapunov泛函获得的结果保守性更低。采用一个基因网络示例来说明所提出理论结果的适用性和有效性。
