Existence of quadratic forms as \(V\)-function of a stable system (Q1178382)
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scientific article; zbMATH DE number 21559
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Existence of quadratic forms as \(V\)-function of a stable system |
scientific article; zbMATH DE number 21559 |
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Existence of quadratic forms as \(V\)-function of a stable system (English)
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26 June 1992
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The author presents (without proofs) two theorems on the solvability of the Lyapunov matrix equation \((1)\;A^ T B+BA=C\) in cases where the matrix \(A\) is stable and \(C\) is positive semidefinite. (If \(B\) is a solution of (1), then \(V(x)=x^ T Bx\) is a Lyapunov function for the linear differential system \(\dot x=Ax\).) Three simple examples are given.
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solvability
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Lyapunov matrix equation
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Lyapunov function
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linear differential system
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examples
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0.9044287
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0.8928189
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0.89181024
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0.88651514
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