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.
This is a preview of subscription content, log in via an institution to check access.
References
Schutz, B.F., 1985, A First Course in General Relativity, Great Britain, Cambridge University Press 160–167.
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.
Schutz, B.F., 1980, Geometrical Methods of Mathematical Physics, Great Britain, Cambridge University Press, chapter 3.
Acknowledgements
Courtesy Department of Electrical Engineering and Mathematics, University of Saskatchewan, Canada: 1986–1989.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Lohar, G. Metric issues for systems in state space. Sādhanā 45, 133 (2020). https://doi.org/10.1007/s12046-020-01361-x
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/s12046-020-01361-x