A revised Kleinman algorithm to solve algebraic Riccati equation of singularly perturbed systems (Q5960326)
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scientific article; zbMATH DE number 1724013
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A revised Kleinman algorithm to solve algebraic Riccati equation of singularly perturbed systems |
scientific article; zbMATH DE number 1724013 |
Statements
A revised Kleinman algorithm to solve algebraic Riccati equation of singularly perturbed systems (English)
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31 October 2002
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Kleinman algorithm
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singularly perturbed systems
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quadratic term
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Riccati equation
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quadratic convergence
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algebraic Lyapunov equation
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numerical algorithm
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The authors show that the Kleinman algorithm can be used well to solve the algebraic Riccati equation of singularly perturbed systems when the quadratic term of the Riccati equation may be indefinite.NEWLINENEWLINENEWLINEThe quadratic convergence property of the Kleinman algorithm is proved by using the Newton-Kantorovich theorem when the initial condition is chosen appropriately. In addition, the numerical method to solve the generalized algebraic Lyapunov equation appearing in the Kleinman algorithm is given. The proposed numerical algorithm can be applied to a control law synthesis involving a solution of an algebraic Riccati equation such as the \(H_2\) and \(H_\infty\) control problem.
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