论文标题
大型自相似网络的频率响应和传递功能
Frequency Response and Transfer Functions of Large Self-similar Networks
论文作者
论文摘要
本文着重于在不同情况下计算大型自相似网络的频率响应和传输功能。通常，由于问题的维度，对大规模系统建模很困难，而自相似性是我们利用的特征，以使问题更加易于处理。对于每种情况，我们都提出算法以获得传输函数和频率响应，并且我们表明有限网络的动态是整数阶的，而无限网络是分数秩序或不合理的。基于这一结果，我们还表明，将网络的工作条件变为其动力学的效果始终可以隔离，然后将其表示为作用于名义工厂的乘法干扰。此外，我们分析了在自相似网络的背景下驻留在无限尺寸系统中的非直集性性质。最后，利用本文的主要结果，我们还说明了其通过使用理性函数近似某些非理性表达的能力。
This paper focuses on computing the frequency response and transfer functions for large self-similar networks under different circumstances. Modeling large scale systems is difficult due, typically, to the dimension of the problem, and self-similarity is the characteristic we exploit to make the problem more tractable. For each circumstance, we propose algorithms to obtain both transfer functions and frequency response, and we show that finite networks' dynamics are integer order, while infinite networks are fractional order or irrational. Based on that result, we also show that the effect of varying a network's operating condition to its dynamics can always be isolated, which is then expressed as a multiplicative disturbance acting upon a nominal plant. In addition, we analyze the non-integer-order nature residing in infinite dimensional systems in the context of self-similar networks. Finally, leveraging the main result of this paper, we also illustrate its capability of approximating some irrational expressions by using rational functions.
