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Volume 3, Issue 3
A Switching Law to Stabilize an Unstable Switched Linear System

Yuhong Zhang, Weisheng Huang & Xiaosong Yang

DOI: 10.12150/jnma.2021.349

J. Nonl. Mod. Anal., 3 (2021), pp. 349-364.

Published online: 2022-06

[An open-access article; the PDF is free to any online user.]

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  • Abstract

Stabilization of switched systems fully composed of unstable modes is of theoretical and practical significance. In this paper, we obtain some sufficient algebraic conditions for stabilizing switched linear systems with all unstable subsystems based on the theory of spherical covering and crystal point groups. Under the proposed algebraic conditions switching laws are easy to be designed to stabilize the switched systems. Some simple examples are provided to illustrate our results.

  • Keywords

Switched system, Unstable mode, Stabilization, Switching law, Spherical covering.

  • AMS Subject Headings

34H15, 93C10, 93C30, 05B40

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JNMA-3-349, author = {Zhang , YuhongHuang , Weisheng and Yang , Xiaosong}, title = {A Switching Law to Stabilize an Unstable Switched Linear System}, journal = {Journal of Nonlinear Modeling and Analysis}, year = {2022}, volume = {3}, number = {3}, pages = {349--364}, abstract = {

Stabilization of switched systems fully composed of unstable modes is of theoretical and practical significance. In this paper, we obtain some sufficient algebraic conditions for stabilizing switched linear systems with all unstable subsystems based on the theory of spherical covering and crystal point groups. Under the proposed algebraic conditions switching laws are easy to be designed to stabilize the switched systems. Some simple examples are provided to illustrate our results.

}, issn = {2562-2862}, doi = {https://doi.org/10.12150/jnma.2021.349}, url = {http://global-sci.org/intro/article_detail/jnma/20666.html} }
TY - JOUR T1 - A Switching Law to Stabilize an Unstable Switched Linear System AU - Zhang , Yuhong AU - Huang , Weisheng AU - Yang , Xiaosong JO - Journal of Nonlinear Modeling and Analysis VL - 3 SP - 349 EP - 364 PY - 2022 DA - 2022/06 SN - 3 DO - http://doi.org/10.12150/jnma.2021.349 UR - https://global-sci.org/intro/article_detail/jnma/20666.html KW - Switched system, Unstable mode, Stabilization, Switching law, Spherical covering. AB -

Stabilization of switched systems fully composed of unstable modes is of theoretical and practical significance. In this paper, we obtain some sufficient algebraic conditions for stabilizing switched linear systems with all unstable subsystems based on the theory of spherical covering and crystal point groups. Under the proposed algebraic conditions switching laws are easy to be designed to stabilize the switched systems. Some simple examples are provided to illustrate our results.

Yuhong Zhang, Weisheng Huang & Xiaosong Yang. (2022). A Switching Law to Stabilize an Unstable Switched Linear System. Journal of Nonlinear Modeling and Analysis. 3 (3). 349-364. doi:10.12150/jnma.2021.349
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