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On the structure of the solution of continuous-time algebraic Riccati equations with closed-loop eigenvalues on the imaginary axis

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Authors
Ntogramatzidis, Lorenzo
Arumugam, V.
Ferrante, A.
Date
2020
Type
Conference Paper

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Ntogramatzidis, L. and Arumugam, V. and Ferrante, A. 2020. On the structure of the solution of continuous-time algebraic Riccati equations with closed-loop eigenvalues on the imaginary axis. In: 21st IFAC World Congress on Automatic Control - Meeting Societal Challenges, 11th Jul 2020, ELECTR NETWORK.
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IFAC-PapersOnLine
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21st IFAC World Congress on Automatic Control - Meeting Societal Challenges
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Faculty
Faculty of Science and Engineering
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School of Elec Eng, Comp and Math Sci (EECMS)
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Abstract

This paper proposes a decomposition of the continuous-time algebraic Riccati equation aimed at eliminating the problem of the presence of closed-loop eigenvalues on the imaginary axis. In particular, we show that it is possible to parameterize the the entire set of solutions of the given Riccati equation in terms of the solutions of a reduced-order Riccati equation, which is associated to a Hamiltonian matrix with no eigenvalues on the imaginary axis, and some free parameters arising from the presence of imaginary eigenvalues of the Hamiltonian matrix.

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