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On the observability of linear, time-invariant systems with unknown inputs

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Abstract

This paper considers the observation of linear, time-invariant dynamical systems in the general case in which some of the input functions are unknown. By arguments based on the concepts of controlled and conditioned invariance, a convenient expression for the observability subspace is found which includes the well-known expression for the case in which the input functions are given.

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References

  1. Kalman, R. E.,Contributions to the Theory of Optimal Control, Boletin de la Societad Matematica Mexicana, Vol. 5, 1960.

  2. Kalman, R. E.,On the General Theory of Control Systems, Proceedings of the First IFAC Congress, Vol. 1, Butterworths, London, 1961.

    Google Scholar 

  3. Kreindler, E., andSarachik, P. E.,On the Concepts of Controllability and Observability in Linear Systems, IEEE Transactions on Automatic Control, Vol. AC-9, No. 2, 1964.

  4. Weiss, L.,The Concepts of Differential Controllability and Differential Observability, Journal of Mathematical Analysis and Applications, Vol. 10, No. 2, 1965.

  5. Silverman, L. M., andMeadows, H. E.,Controllability and Observability in Time-Variable Linear Systems, SIAM Journal on Control, Vol. 5, No. 1, 1967.

  6. Basile, G., andMarro, G.,Controlled and Conditioned Invariant Subspaces in Linear System Theory, Journal of Optimization Theory and Applications, Vol. 3, No. 5, 1969.

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Communicated by G. Leitmann

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Basile, G., Marro, G. On the observability of linear, time-invariant systems with unknown inputs. J Optim Theory Appl 3, 410–415 (1969). https://doi.org/10.1007/BF00929356

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  • DOI: https://doi.org/10.1007/BF00929356

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