In this article, we present a stability analysis of linear time-invariant systems in control theory. The linear time-invariant systems under consideration involve the diagonal norm bounded linear differential inclusions. We propose a methodology based on low-rank ordinary differential equations. We construct an equivalent time-invariant system (linear) and use it to acquire an optimization problem whose solutions are given in terms of a system of differential equations. An iterative method is then used to solve the system of differential equations. The stability of linear time-invariant systems with diagonal norm bounded differential inclusion is studied by analyzing the Spectrum of equivalent systems.

中文翻译：

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具有对角范数有界线性微分包含的LTI系统的稳定性分析

在本文中，我们根据控制理论对线性时不变系统进行了稳定性分析。所考虑的线性时不变系统涉及对角范数有界线性微分包含。我们提出了一种基于低阶常微分方程的方法。我们构造了一个等效的时不变系统（线性），并使用它来获取一个优化问题，该问题的解以微分方程组的形式给出。然后使用迭代方法求解微分方程组。通过分析等效系统的频谱，研究了具有对角范数有界包容性的线性时不变系统的稳定性。