Self-bounded controlled invariants versus stabilizability |
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Authors: | G Basile G Marro |
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Institution: | (1) Department of Electrical Engineering, University of Florida, Gainesville, Florida;(2) Department of Electronics, Computers, and Systems, University of Bologna, Bologna, Italy |
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Abstract: | Self-bounded controlled and self-hidden conditioned invariant subspaces, recently introduced by the authors for a more direct and neat handling of some fundamental concepts of the geometric approach, such as controllability subspaces, are proved in this paper to be very useful tools also in dealing with synthesis problems with stability requirements.Definitions concerning stability of invariants and stabilizability of controlled invariants, simple and self-bounded, are first presented and discussed. In particular, it is shown that a more straightforward definition for controlled invariant stabilizability allows a simpler development of the theory, Then, some fundamental results relating self-boundedness to stabilizability are derived. For the sake of completeness, all statements are dualized to conditioned invariants, simple and self-hidden. |
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Keywords: | Controlled invariants (A )-invariants" target="_blank">gif" alt="bernou" align="MIDDLE" BORDER="0">)-invariants conditioned invariants ( " target="_blank">gif" alt="Lscr" align="MIDDLE" BORDER="0"> A)-invariants stability stabilizability geometric approach linear system theory |
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