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Solvability Criterion for the Constrained Discrete Lyapunov and Riccati Equations

Author

Listed:
  • N. Sharav-Schapiro

    (Technion-Israel Institute of Technology)

  • Z. J. Palmor

    (Technion-Israel Institute of Technology)

  • A. Steinberg

    (Technion-Israel Institute of Technology)

Abstract

Conditions for the solvability of the discrete Lyapunov and the discrete Riccati equations subject to linear equality constraints are derived. These problems arise naturally in the context of output min-max robust control. It is shown that the following problems are equivalent to one another: (a) the solvability of the constrained discrete Riccati equation; and (b) the existence of a feedback gain that guarantees the solvability of the constrained discrete Lyapunov equation of the resulting closed loop. A simple criterion for the existence of a solution to both problems is presented. These problems are shown to be related to the discrete positive real property.

Suggested Citation

  • N. Sharav-Schapiro & Z. J. Palmor & A. Steinberg, 1997. "Solvability Criterion for the Constrained Discrete Lyapunov and Riccati Equations," Journal of Optimization Theory and Applications, Springer, vol. 92(1), pages 149-160, January.
    • Handle: RePEc:spr:joptap:v:92:y:1997:i:1:d:10.1023_a:1022644231318
    DOI: 10.1023/A:1022644231318
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    Cited by:

    1. N. Sharav-Schapiro & Z. J. Palmor & A. Steinberg, 1999. "Dynamic Robust Output Min–Max Control for Discrete Uncertain Systems," Journal of Optimization Theory and Applications, Springer, vol. 103(2), pages 421-439, November.

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