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Frontiers of Information Technology & Electronic Engineering
ISSN 2095-9184 (print), ISSN 2095-9230 (online)
2021 Vol.22 No.2 P.210-221
Solution and stability of continuous-time cross-dimensional linear systems
Abstract: We investigate the solution and stability of continuous-time cross-dimensional linear systems (CCDLSs) with dimension bounded by V-addition and V-product. Using the integral iteration method, the solution to CCDLSs can be obtained. Based on the new algebraic expression of the solution and the Jordan decomposition method of matrix, a necessary and sufficient condition is derived for judging whether a CCDLS is asymptotically stable with a given initial state. This condition demonstrates a method for finding the domain of attraction and its relationships. Then, all the initial states that can be stabilized are studied, and a method for designing the corresponding controller is proposed. Two examples are presented to illustrate the validity of the theoretical results.
Key words: Cross-dimensional, V-addition, V-product, Asymptotic stability, Stabilization
张庆乐，王彪，冯俊娥
山东大学数学学院，中国济南市，250100
摘要：利用V-加法和V-乘法研究了维数有界的跨维数线性连续系统（CCDLSs）的解和稳定性。使用积分迭代法，得到CCDLSs的解。基于解的代数表示以及矩阵的若尔当分解，给出相应的充要条件判断一个CCDLS在给定初始状态后是否渐进稳定。该条件提供了一种确定吸引域以及吸引域间关系的方法。然后，研究了所有可镇定的初始状态，并提出相应控制器的设计方法。最后，给出两个例子说明理论结果的有效性。
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DOI:
10.1631/FITEE.1900504
CLC number:
O231
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On-line Access:
2021-02-01
Received:
2019-09-19
Revision Accepted:
2020-06-15
Crosschecked:
2020-08-19