带比例导数控制器的阻尼线性微分方程的非振动性及其在whittaker - hill型和mathieu型方程中的应用

IF 1 Q1 MATHEMATICS
Kazuki Ishibashi
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引用次数: 0

摘要

微分算子的比例导数(PD)控制器通常被称为适形导数。本文利用控制论的适形导数,导出了一类含微分算子的阻尼线性微分方程的非振荡定理。非振荡定理的证明利用了与所考虑的方程相对应的里卡蒂不等式。所提供的非振荡定理给出了带PD控制器的阻尼欧拉型微分方程的非振荡条件。此外,本文还考虑了具有可推广whittaker - hill型方程的PD控制器的方程的非振荡问题。本研究考虑的whittaker - hill型方程还包括mathieu型方程。作为本工作的一个子课题,我们在充分利用数值模拟的同时,考虑了带PD控制器的mathieu型方程的非振荡问题。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Nonoscillation of damped linear differential equations with a proportional derivative controller and its application to Whittaker-Hill-type and Mathieu-type equations
The proportional derivative (PD) controller of a differential operator is commonly referred to as the conformable derivative. In this paper, we derive a nonoscillation theorem for damped linear differential equations with a differential operator using the conformable derivative of control theory. The proof of the nonoscillation theorem utilizes the Riccati inequality corresponding to the equation considered. The provided nonoscillation theorem gives the nonoscillatory condition for a damped Euler-type differential equation with a PD controller. Moreover, the nonoscillation of the equation with a PD controller that can generalize Whittaker-Hill-type equations is also considered in this paper. The Whittaker-Hill-type equation considered in this study also includes the Mathieu-type equation. As a subtopic of this work, we consider the nonoscillation of Mathieu-type equations with a PD controller while making full use of numerical simulations.
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来源期刊
Opuscula Mathematica
Opuscula Mathematica MATHEMATICS-
CiteScore
1.70
自引率
20.00%
发文量
30
审稿时长
22 weeks
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