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Entropy and random feedback

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Open Problems in Mathematical Systems and Control Theory

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

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Abstract

Let C ∈ Cm×n. The Frobenius norm of C is defined as

$$ {\left\| C \right\|_F} = \sqrt {TrC{C^ * }} ,$$

where C* denotes the complex-conjugate transpose and Tr denotes trace. The spectral norm of C is defined as

$$ \left\| C \right\| = \sqrt {{\lambda _{\max }}\left( {C{C^ * }} \right)} , $$

where λmax denotes the maximum eigenvalue.

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References

  1. S. Boyd and C. Barratt. Linear Controller Design: Limits of Performance. Prentice-Hall, 1991.

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  2. Mustafa and K. Glover. Minimum Entropy H∞ Control Lecture Notes in Control and Information Sciences. Springer-Verlag, 1990.

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  3. Yu. Nesterov and A. Nemirovsky. Interior-point polynomial methods in convex programming, volume 13 of Studies in Applied Mathematics. SIAM, Philadelphia, PA, 1994.

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  4. L. Vandenberghe and S. Boyd. Semidefinite programming. SIAM Review,, 38 (l): 49–95, March 1996.

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  5. L. Vandenberghe, S. Boyd, and S.-P. Wu. Determinant maximization with linear matrix inequality constraints. SIAM J. on Matrix Analysis and Applications, April 1998. To appear.

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Author information

Authors and Affiliations

  1. Information Systems Laboratory Electrical Engineering Department, Stanford University, Stanford, CA, 94305, USA

    Stephen P. Boyd

Authors
  1. Stephen P. Boyd
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Editor information

Editors and Affiliations

  1. Institute of Mathematics, University of Leige, Sart Tilman B37, B-4000, Liege, Belgium

    Vincent Blondel (PhD) (PhD)

  2. Department of Mathematics, Rutgers University, Hill Center 724, 08903, New Brunswick, USA

    Eduardo D. Sontag (PhD) (PhD)

  3. Centre for Arificial Intelligence and Robotics, Raj Bhavan Cirlce - High Grounds, 560001, Bangalore, India

    Mathukumalli Vidyasagar (PhD) (PhD)

  4. Institute of Mathematics, Rijksuniversiteit te Groningen, Postbus 800, 9700, Av Groningen, The Netherlands

    Jan C. Willems (PhD) (PhD)

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© 1999 Springer-Verlag London Limited

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Boyd, S.P. (1999). Entropy and random feedback. In: Blondel, V., Sontag, E.D., Vidyasagar, M., Willems, J.C. (eds) Open Problems in Mathematical Systems and Control Theory. Communications and Control Engineering. Springer, London. https://doi.org/10.1007/978-1-4471-0807-8_15

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  • DOI: https://doi.org/10.1007/978-1-4471-0807-8_15

  • Publisher Name: Springer, London

  • Print ISBN: 978-1-4471-1207-5

  • Online ISBN: 978-1-4471-0807-8

  • eBook Packages: Springer Book Archive

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