Exponential Stability and Relative Controllability of Nonsingular Conformable Delay Systems

IF 1.9 3区数学 Q1 MATHEMATICS, APPLIED

Axioms Pub Date : 2023-10-20 DOI:10.3390/axioms12100994

Airen Zhou

引用次数: 0

Abstract

In this paper, we investigate a delayed matrix exponential and utilize it to derive a representation of solutions to a linear nonsingular delay problem with permutable matrices. To begin with, we present a novel definition of α-exponential stability for these systems. Subsequently, we put forward several adequate conditions to ensure the α-exponential stability of solutions for such delay systems. Moreover, by constructing a Grammian matrix that accounts for delays, we provide a criterion to determine the relative controllability of a linear problem. Additionally, we extend our analysis to nonlinear problems. Lastly, we offer several examples to verify the effectiveness of our theoretical findings.

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非奇异相容时滞系统的指数稳定性和相对可控性

本文研究了一类时滞矩阵指数，并利用它导出了一类具有可变矩阵的线性非奇异时滞问题的解的表示。首先，我们给出了这些系统α-指数稳定性的一个新的定义。随后，我们给出了保证这类时滞系统解的α-指数稳定性的几个充分条件。此外，通过构造一个考虑延迟的Grammian矩阵，我们提供了一个标准来确定线性问题的相对可控性。此外，我们将我们的分析扩展到非线性问题。最后，我们提供了几个例子来验证我们的理论发现的有效性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Axioms Mathematics-Algebra and Number Theory

自引率

10.00%

发文量

604

审稿时长

11 weeks

期刊介绍： Axiomatic theories in physics and in mathematics (for example, axiomatic theory of thermodynamics, and also either the axiomatic classical set theory or the axiomatic fuzzy set theory) Axiomatization, axiomatic methods, theorems, mathematical proofs Algebraic structures, field theory, group theory, topology, vector spaces Mathematical analysis Mathematical physics Mathematical logic, and non-classical logics, such as fuzzy logic, modal logic, non-monotonic logic. etc. Classical and fuzzy set theories Number theory Systems theory Classical measures, fuzzy measures, representation theory, and probability theory Graph theory Information theory Entropy Symmetry Differential equations and dynamical systems Relativity and quantum theories Mathematical chemistry Automata theory Mathematical problems of artificial intelligence Complex networks from a mathematical viewpoint Reasoning under uncertainty Interdisciplinary applications of mathematical theory.