Metric issues for systems in state space

Abstract

A metric structure is imposed on state space such that solutions to 1st order state variable model of a linear system are geodesics subject to restrictions on the system and input matrices. For linear time invariant systems, a 2nd order state variable model of an extended system to a given 1st order model is derived. The metric is tailored to systems under consideration.

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References

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    Schutz, B.F., 1985, A First Course in General Relativity, Great Britain, Cambridge University Press 160–167.

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    Santina, M.S., Stubberud, A.R., Hostetter, G.H., 1994, Digital Control System Design, 2nd edition, United States of America, Saunders College Publishing 109–128.

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    Schutz, B.F., 1980, Geometrical Methods of Mathematical Physics, Great Britain, Cambridge University Press, chapter 3.

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Acknowledgements

Courtesy Department of Electrical Engineering and Mathematics, University of Saskatchewan, Canada: 1986–1989.

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Correspondence to Gautam Lohar.

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Lohar, G. Metric issues for systems in state space. Sādhanā 45, 133 (2020). https://doi.org/10.1007/s12046-020-01361-x

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Keywords

  • Linear system
  • state variable
  • state space
  • metric
  • geodesic