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Feedback invariance of SISO infinite-dimensional systems

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Abstract

We consider a linear single-input single-output system on a Hilbert space X, with infinitesimal generator A, bounded control element b, and bounded observation element c. We address the problem of finding the largest feedback invariant subspace of X that is in the space c ⊥ perpendicular to c. If b is not in c ⊥, we show this subspace is c ⊥. If b is in c ⊥, a number of situations may occur, depending on the relationship between b and c.

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Authors and Affiliations

  1. Department of Applied Mathematics, University of Waterloo, 200 University Ave. W., Waterloo, ON, N2L 3G1, Canada

    Kirsten Morris

  2. Department of Mathematics, University of Nebraska, Lincoln, USA

    Richard Rebarber

Authors
  1. Kirsten Morris
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  2. Richard Rebarber
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Correspondence to Kirsten Morris.

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Morris, K., Rebarber, R. Feedback invariance of SISO infinite-dimensional systems. Math. Control Signals Syst. 19, 313–335 (2007). https://doi.org/10.1007/s00498-007-0021-9

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  • DOI: https://doi.org/10.1007/s00498-007-0021-9

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