A necessary and sufficient condition in Lyapunov robust control (Q1115386)
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scientific article; zbMATH DE number 4085512
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A necessary and sufficient condition in Lyapunov robust control |
scientific article; zbMATH DE number 4085512 |
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A necessary and sufficient condition in Lyapunov robust control (English)
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1989
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We consider Lyapunov's equation \(PA+A^ TP+Q=0\), where Q is symmetric positive definite and A is in controllable companion form. We prove that a necessary and sufficient condition that A be stable is that the first row \(P_ 1\) of the P-matrix be a stable n-1 coefficient vector. This result is related to the minimum phase property of linear systems and is useful in designing robust controllers.
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Lyapunov's equation
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controllable companion form
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necessary and sufficient condition
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robust controllers
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