Explicit Commutativity for Lamé Linear Time-Varying Differential Systems

IF 1.6 4区工程技术 Q3 ENGINEERING, ELECTRICAL & ELECTRONIC International Journal of Numerical Modelling-Electronic Networks Devices and Fields Pub Date : 2024-11-11 DOI:10.1002/jnm.3309

Salisu Ibrahim, Salah Boulaaras, Abedallah Rababah, Mujahid Iqbal

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Abstract

This article studies the commutativity and sensitivity of the Lamé linear time-varying systems (LTVSs), and investigates the effects of disturbances on such systems. The commutative pair for the Lamé LTVS $A$ of order $2$ is found, that is, a new Lamé LTVS $B$ of order $m \leq 2$ is derived using the explicit commutative theories for zero initial conditions (ICs). For the case of nonzero ICs, the commutativity between the connected input–output of Lamé systems $AB$ and $BA$ is studied. New and simple explicit commutative theories and conditions for second-order LTVSs are derived, simplifying the use of commutativity for practical and industrial scenarios. These findings enable us to analyse the commutativity, sensitivity, robustness and stability of Lamé systems, and to determine the effects of disturbances. The explicit results presented in this article are supported by simulations and verified by examples and constitute a significant contribution to science and engineering applications.

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拉美线性时变微分系统的显式换元性

本文研究了拉梅线性时变系统（LTVS）的换元性和敏感性，并探讨了干扰对此类系统的影响。利用零初始条件（ICs）的显式换元理论，找到了阶数为 2 $$ 2 $$ 的拉梅 LTVS A $$ A $$ 的换元对，即推导出了阶数为 m ≤ 2 $$ m\le 2 $$ 的新拉梅 LTVS B $$ B $$。对于非零初始条件，研究了拉美系统 AB $$ AB $$ 和 BA $$ BA $$ 的连接输入输出之间的换元性。为二阶 LTVS 推导出了新的、简单明确的换向理论和条件，简化了换向性在实际和工业场景中的应用。这些发现使我们能够分析拉美系统的换向性、敏感性、鲁棒性和稳定性，并确定干扰的影响。本文提出的明确结果得到了模拟的支持和实例的验证，是对科学和工程应用的重大贡献。

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来源期刊

International Journal of Numerical Modelling-Electronic Networks Devices and Fields 工程技术-工程：电子与电气

CiteScore

4.60

自引率

6.20%

发文量

101

审稿时长

>12 weeks

期刊介绍： Prediction through modelling forms the basis of engineering design. The computational power at the fingertips of the professional engineer is increasing enormously and techniques for computer simulation are changing rapidly. Engineers need models which relate to their design area and which are adaptable to new design concepts. They also need efficient and friendly ways of presenting, viewing and transmitting the data associated with their models. The International Journal of Numerical Modelling: Electronic Networks, Devices and Fields provides a communication vehicle for numerical modelling methods and data preparation methods associated with electrical and electronic circuits and fields. It concentrates on numerical modelling rather than abstract numerical mathematics. Contributions on numerical modelling will cover the entire subject of electrical and electronic engineering. They will range from electrical distribution networks to integrated circuits on VLSI design, and from static electric and magnetic fields through microwaves to optical design. They will also include the use of electrical networks as a modelling medium.