Abstract
The equivalence of two conditions, condition (3) and condition (4) stated in Problem Statement section, regarding the existence of stabilizing switching laws between two unstable linear systems first appeared in (Feron 1996). Although Feron never published this result, it has been referenced in almost every survey on switched systems; see, for example, (Liberzon and Morse 1999). This paper proposes another way to prove the equivalence of two conditions regarding the existence of stabilizing switching laws between two unstable linear systems. One is effective for theoretical derivation, while the other is implementable, and a class of stabilizing switching laws have been explicitly constructed by Wicks et al. (1994). With the help of the equivalent relation, a condition for the existence of controllers and stabilizing switching laws between two unstabilizable linear control systems is then proposed. Then, the study is further extended to the issue concerning the construction of quadratically stabilizing switching laws among N unstable linear systems and N unstabilizable linear control systems. The obtained results are employed to study the existence of control laws and quadratically stabilizing switching laws within a class of unstabilizable linear control systems. The numerical examples are illustrated and simulated to show the feasibility and effectiveness of the proposed methods.
| Original language | English |
|---|---|
| Article number | 681523 |
| Journal | Abstract and Applied Analysis |
| Volume | 2013 |
| DOIs | |
| Publication status | Published - 2013 Dec 6 |
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All Science Journal Classification (ASJC) codes
- Analysis
- Applied Mathematics
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On existence of stabilizing switching laws within a class of unstable linear systems. / Xu, Sendren Sheng Dong; Chen, Chih Chiang.
In: Abstract and Applied Analysis, Vol. 2013, 681523, 06.12.2013.Research output: Contribution to journal › Article
TY - JOUR
T1 - On existence of stabilizing switching laws within a class of unstable linear systems
AU - Xu, Sendren Sheng Dong
AU - Chen, Chih Chiang
PY - 2013/12/6
Y1 - 2013/12/6
N2 - The equivalence of two conditions, condition (3) and condition (4) stated in Problem Statement section, regarding the existence of stabilizing switching laws between two unstable linear systems first appeared in (Feron 1996). Although Feron never published this result, it has been referenced in almost every survey on switched systems; see, for example, (Liberzon and Morse 1999). This paper proposes another way to prove the equivalence of two conditions regarding the existence of stabilizing switching laws between two unstable linear systems. One is effective for theoretical derivation, while the other is implementable, and a class of stabilizing switching laws have been explicitly constructed by Wicks et al. (1994). With the help of the equivalent relation, a condition for the existence of controllers and stabilizing switching laws between two unstabilizable linear control systems is then proposed. Then, the study is further extended to the issue concerning the construction of quadratically stabilizing switching laws among N unstable linear systems and N unstabilizable linear control systems. The obtained results are employed to study the existence of control laws and quadratically stabilizing switching laws within a class of unstabilizable linear control systems. The numerical examples are illustrated and simulated to show the feasibility and effectiveness of the proposed methods.
AB - The equivalence of two conditions, condition (3) and condition (4) stated in Problem Statement section, regarding the existence of stabilizing switching laws between two unstable linear systems first appeared in (Feron 1996). Although Feron never published this result, it has been referenced in almost every survey on switched systems; see, for example, (Liberzon and Morse 1999). This paper proposes another way to prove the equivalence of two conditions regarding the existence of stabilizing switching laws between two unstable linear systems. One is effective for theoretical derivation, while the other is implementable, and a class of stabilizing switching laws have been explicitly constructed by Wicks et al. (1994). With the help of the equivalent relation, a condition for the existence of controllers and stabilizing switching laws between two unstabilizable linear control systems is then proposed. Then, the study is further extended to the issue concerning the construction of quadratically stabilizing switching laws among N unstable linear systems and N unstabilizable linear control systems. The obtained results are employed to study the existence of control laws and quadratically stabilizing switching laws within a class of unstabilizable linear control systems. The numerical examples are illustrated and simulated to show the feasibility and effectiveness of the proposed methods.
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UR - http://www.scopus.com/inward/citedby.url?scp=84888881105&partnerID=8YFLogxK
U2 - 10.1155/2013/681523
DO - 10.1155/2013/681523
M3 - Article
AN - SCOPUS:84888881105
VL - 2013
JO - Abstract and Applied Analysis
JF - Abstract and Applied Analysis
SN - 1085-3375
M1 - 681523
ER -