Solution and stability of continuous-time cross-dimensional linear systems

2021, Volume 22, Issue 2

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Frontiers of Information Technology & Electronic Engineering >> 2021, Volume 22, Issue 2 doi: 10.1631/FITEE.1900504

Solution and stability of continuous-time cross-dimensional linear systems

山东大学数学学院，中国济南市，250100

Received: 2019-09-19 Accepted: 2021-02-01 Available online: 2021-02-01

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Abstract

We investigate the solution and stability of continuous-time linear systems (CCDLSs) with dimension bounded by and . 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.

Keywords

Cross-dimensional ; V-addition ; V-product ; Asymptotic stability ; Stabilization

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