On the Lyapunov equation in Banach spaces and applications to control problems (Q1607829)
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scientific article; zbMATH DE number 1780328
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the Lyapunov equation in Banach spaces and applications to control problems |
scientific article; zbMATH DE number 1780328 |
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On the Lyapunov equation in Banach spaces and applications to control problems (English)
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13 August 2002
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The authors consider the equivalence between the solvability of the Lyapunov equation and exponential stability of a linear system in a Banach space. Moreover they establish the relationship between stabilizability and exact null-controllability of linear control systems and then give some applications to the exponential stabilizability of a class of nonlinear control systems in Banach space by using the Lyapunov theorem. The results of this paper can be considered as a further development of results obtained earlier.
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Lyapunov equation
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exponential stability
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stabilizability
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exact null-controllability
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