On Existence of Stabilizing Switching Laws within a Class of Unstable Linear Systems
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 almo...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2013-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2013/681523 |
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| Summary: | 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 unstable linear
systems and 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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| ISSN: | 1085-3375 1687-0409 |