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Linear Riccati Dynamics, Constant Feedback, and Controllability in Linear Quadratic Control Problems

Author

Listed:
  • Ronald J. Balvers

    (Department of Economics, West Virginia University)

  • Douglas W. Mitchell

    (Department of Economics, West Virginia University)

Abstract

Conditions are derived for linear-quadratic control (LQC) problems to exhibit linear evolution of the Riccati matrix and constancy of the control feedback matrix. One of these conditions involves a matrix upon whose rank a necessary condition and a sufficient condition for controllability are based. Linearity of Riccati evolution allows for rapid iterative calculation, and constancy of the control feedback matrix allows for time-invariant comparative static analysis of policy reactions.

Suggested Citation

  • Ronald J. Balvers & Douglas W. Mitchell, 2005. "Linear Riccati Dynamics, Constant Feedback, and Controllability in Linear Quadratic Control Problems," Working Papers 05-10 Classification- JEL, Department of Economics, West Virginia University.
  • Handle: RePEc:wvu:wpaper:05-10
    as

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    File URL: http://be.wvu.edu/phd_economics/pdf/05-10.pdf
    File Function: First version, 2005
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    References listed on IDEAS

    as
    1. Anderson, Evan W. & McGrattan, Ellen R. & Hansen, Lars Peter & Sargent, Thomas J., 1996. "Mechanics of forming and estimating dynamic linear economies," Handbook of Computational Economics,in: H. M. Amman & D. A. Kendrick & J. Rust (ed.), Handbook of Computational Economics, edition 1, volume 1, chapter 4, pages 171-252 Elsevier.
    2. Blanchard, Olivier Jean & Kahn, Charles M, 1980. "The Solution of Linear Difference Models under Rational Expectations," Econometrica, Econometric Society, vol. 48(5), pages 1305-1311, July.
    3. Anderson, Gary & Moore, George, 1985. "A linear algebraic procedure for solving linear perfect foresight models," Economics Letters, Elsevier, vol. 17(3), pages 247-252.
    4. Ehlgen, Jurgen, 1999. "A Nonrecursive Solution Method for the Linear-Quadratic Optimal Control Problem with a Singular Transition Matrix," Computational Economics, Springer;Society for Computational Economics, vol. 13(1), pages 17-23, February.
    5. Klein, Paul, 2000. "Using the generalized Schur form to solve a multivariate linear rational expectations model," Journal of Economic Dynamics and Control, Elsevier, vol. 24(10), pages 1405-1423, September.
    6. Binder, Michael & Pesaran, Hashem, 2000. "Solution of finite-horizon multivariate linear rational expectations models and sparse linear systems," Journal of Economic Dynamics and Control, Elsevier, vol. 24(3), pages 325-346, March.
    7. Hans M. Amman & David A. Kendrick, . "Computational Economics," Online economics textbooks, SUNY-Oswego, Department of Economics, number comp1, March.
    Full references (including those not matched with items on IDEAS)

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    Keywords

    Controllability; Riccati Equation; Linear Quadratic Control.;

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