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Invariant Subspace Methods for the Numerical Solution of Riccati Equations

  • Chapter
The Riccati Equation

Part of the book series: Communications and Control Engineering Series ((CCE))

Abstract

In this tutorial paper, an overview is given of progress over the past ten to fifteen years towards reliable and efficient numerical solution of various types of Riccati equations. Our attention will be directed primarily to matrix-valued algebraic Riccati equations and numerical methods for their solution based on computing bases for invariant subspaces of certain associated matrices. Riccati equations arise in modeling both continuous-time and discrete-time systems in a wide variety of applications in science and engineering. One can study both algebraic equations and differential or difference equations. Both algebraic and differential or difference equations can be further classified according to whether their coefficient matrices give rise to so-called symmetric or nonsymmetric equations. Symmetric Riccati equations can be further classified according to whether or not they are definite or indefinite.

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  1. Alan J. Laub
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  1. Dipartimento di Elettronica, Politecnico di Milano, Piazza Leonardo da Vinci 32, I-20133, Milano, Italy

    Sergio Bittanti

  2. Department of Electrical and Computer Engineering, University of California, Santa Barbara, CA, 93106, USA

    Alan J. Laub

  3. Department of Mathematics, University of Groningen, P.O. Box 800, NL-9700 AV, Groningen, The Netherlands

    Jan C. Willems

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Laub, A.J. (1991). Invariant Subspace Methods for the Numerical Solution of Riccati Equations. In: Bittanti, S., Laub, A.J., Willems, J.C. (eds) The Riccati Equation. Communications and Control Engineering Series. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-58223-3_7

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