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Theory and Numerical Solution of Differential and Algebraic Riccati Equations

In: Numerical Algebra, Matrix Theory, Differential-Algebraic Equations and Control Theory

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  • Peter Benner

    (Max Planck Institute for Dynamics of Complex Technical Systems)

Abstract

Since Kalman’s seminal work on linear-quadratic control and estimation problems in the early 1960s, Riccati equations have been playing a central role in many computational methods for solving problems in systems and control theory, like controller design, Kalman filtering, model reduction, and many more. We will review some basic theoretical facts as well as computational methods to solve them, with a special emphasis on the many contributions Volker Mehrmann had regarding these subjects.

Suggested Citation

  • Peter Benner, 2015. "Theory and Numerical Solution of Differential and Algebraic Riccati Equations," Springer Books, in: Peter Benner & Matthias Bollhöfer & Daniel Kressner & Christian Mehl & Tatjana Stykel (ed.), Numerical Algebra, Matrix Theory, Differential-Algebraic Equations and Control Theory, edition 127, chapter 0, pages 67-105, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-15260-8_4
    DOI: 10.1007/978-3-319-15260-8_4
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