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数学与物理
应用数学进展
Vol. 12 No. 6 (June 2023)
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一种新型的混合系统
A Novel Hybrid System
DOI:
10.12677/AAM.2023.126266
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被引量
作者:
魏金飞
:浙江师范大学,数学科学学院,浙江 金华
关键词:
脉冲系统
;
逻辑动态系统
;
矩阵的半张量积
;
稳定性
;
Impulsive System
;
Logical Dynamic System
;
The Semi Tensor Product of Matrices
;
Stability
摘要:
脉冲系统作为一类混杂系统,可以与逻辑动态系统相结合,研究逻辑选择脉冲效应的系统。 由于动力系统由脉冲效应和逻辑运算组成,因此它们是更一般和更复杂的混合系统。 运用矩阵的半张 量积的方法,将逻辑函数转换为等价的代数形式,使这类脉冲系统的研究成为可能。 本文主要运用矩阵的半张量积的方法将脉冲系统与逻辑动态系统结合。
Abstract:
Impulsive systems, as a type of hybrid system, can be combined with logical dynamic systems to study systems with logic selective impulsive effects. Due to the fact that the power system consists of impulsive effects and logical operations, they are more general and complex hybrid systems. By using the semi-tensor product method of matrices,the logical function is transformed into an equivalent algebraic form, making the study of such impulsive systems possible. This article mainly uses the semi tensor product method of matrices to combine impulsive systems with logical dynamic systems.
文章引用:
魏金飞. 一种新型的混合系统[J]. 应用数学进展, 2023, 12(6): 2643-2649.
https://doi.org/10.12677/AAM.2023.126266
参考文献
[1]
Benchohra, M., Henderson, J. and Ntouyas, S. (2006) Impulsive Differential Equations and In- clusions. Hindawi Publishing Corporation, New York.
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Ballinger, G. and Liu, X.Z. (1999) Existence and Uniqueness Results for Impulsive Delay Differential Equations. Dynamics of Continuous Discrete and Impulsive Systems, 5, 579-591.
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Liu, X. and Ballinger, G. (2003) Boundedness for Impulsive Delay Differential Equations and Applications to Population Growth Models. Nonlinear Analysis: Theory, Methods & Applica- tions, 53, 1041-1062.
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[4]
Wang, Q. and Liu, X. (2005) Exponential Stability for Impulsive Delay Differential Equations by Razumikhin Method. Journal of Mathematical Analysis and Applications, 309, 462-473.
https://doi.org/10.1016/j.jmaa.2004.09.016
[5]
Li, X. (2010) New Results on Global Exponential Stabilization of Impulsive Functional D- ifferential Equations with Infinite Delays or Finite Delays. Nonlinear Analysis: Real World Applications, 11, 4194-4201.
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[6]
Li, X. and Song, S. (2016) Stabilization of Delay Systems: Delay-Dependent Impulsive Control. IEEE Transactions on Automatic Control, 62, 406-411.
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Cheng, D.Z., Qi, H.S. and Li, Z.Q. (2011) Analysis and Control of Boolean Networks: A Semitensor Product Approach. Springer, New York.
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