IEEE Trans Neural Netw Learn Syst. 2018 Aug;29(8):3404-3417. doi: 10.1109/TNNLS.2017.2721448. Epub 2017 Aug 7.
The model approximation problem is studied in this paper for switched genetic regulatory networks (GRNs) with time-varying delays. We focus on constructing a reduced-order model to approximate the high-order GRNs considered under the switching signal subject to certain constraints, such that the approximation error system between the original and reduced-order systems is exponentially stable with a disturbance attenuation performance. The stability conditions and the disturbance attenuation performance are established by utilizing two integral inequality bounding techniques and the average dwell-time method for the approximation error system. Then, the solvability conditions for the reduced-order models for the GRNs are also established using the projection method. Furthermore, the model approximation problem can be transferred into a sequential minimization problem that is subject to linear matrix inequality constraints by using the cone complementarity algorithm. Finally, several examples are provided to illustrate the effectiveness and the advantages of the proposed methods.
本文针对时变时滞切换基因调控网络（GRNs），研究了模型逼近问题。我们专注于构建一个降阶模型来逼近在切换信号下考虑的高阶 GRNs，同时满足某些约束条件，使得原系统和降阶系统之间的逼近误差系统具有指数稳定性和干扰衰减性能。通过利用两个积分不等式边界技术和平均驻留时间方法，为逼近误差系统建立了稳定性条件和干扰衰减性能。然后，利用投影方法，为 GRNs 的降阶模型建立了可解性条件。此外，通过使用锥互补算法，可以将模型逼近问题转化为一个满足线性矩阵不等式约束的序列最小化问题。最后，通过几个例子来说明所提出方法的有效性和优势。
