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IMA Journal of Mathematical Control and Information 1992 9(3):255-263; doi:10.1093/imamci/9.3.255
© 1992 by Institute of Mathematics and its Applications
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Stability and stabilizability of linear infinite-dimensional discrete-time systems

HARTMUT LOGEMANN

Institut für Dynamische Systeme, Universität Bremen Postfach 330 440, 2800 Bremen 33, Germany

This paper contains three results on stability and stabilizability of linear time invariant infinite-dimensional discrete-time systems. (1) Power stability is characterized in transfer-function terms using the concepts of stabilizability and detectability. (2) Under the assumption that the input operator is campact, we present a necessary and sufficient condition for stabilizability involving spectral properties of the system operator and a projection of the infinite-dimensional system onto a certain finite-dimensional subspace of the state space. (3) It is shown that, if the input and output spaces are finite-dimensional, then stabilization by finite-dimensional dynamic output feedback is possible if and only if the systems is detectable and stabilizable.


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