论文标题
$ l_2 $诱导非负输入信号的离散时间LTI系统及其应用于复发性神经网络的稳定性分析
$l_2$ Induced Norm Analysis of Discrete-Time LTI Systems for Nonnegative Input Signals and Its Application to Stability Analysis of Recurrent Neural Networks
论文作者
论文摘要
在本文中，我们专注于“正则” $ l_2 $引起的离散时间线性时间流动系统的规范，在该系统中，输入信号仅限于无负。为了应对输入信号的非负性，我们采用共同编程作为分析的数学工具。然后，通过将内部近似值应用于共阳性锥，我们得出了可用于数值拖延的半决赛编程问题，以用于“正” $ L_2 $诱导的Norm的上限和下限计算。该规范通常对于由LTI系统构建的反馈系统和非线性元素仅提供非负信号的非线性构建的反馈系统的稳定性分析通常很有用。作为一个具体的示例，我们说明了“正” $ L_2 $诱导的规范对复发性神经网络的稳定性分析的有用性，其激活函数是整流的线性单元。
In this paper, we focus on the "positive" $l_2$ induced norm of discrete-time linear time-invariant systems where the input signals are restricted to be nonnegative. To cope with the nonnegativity of the input signals, we employ copositive programming as the mathematical tool for the analysis. Then, by applying an inner approximation to the copositive cone, we derive numerically tractable semidefinite programming problems for the upper and lower bound computation of the "positive" $l_2$ induced norm. This norm is typically useful for the stability analysis of feedback systems constructed from an LTI system and nonlinearities where the nonlinear elements provide only nonnegative signals. As a concrete example, we illustrate the usefulness of the "positive" $l_2$ induced norm for the stability analysis of recurrent neural networks with activation functions being rectified linear units.
