Abstract
Given a system pair (A, B) we consider all pairs (A + BF, BG) which can be formed by means of state feedback F and the connection of a ‘gain’ matrix G at the system input (Fig. 5.1). The controllable subspace of (A + BF, BG) is called a controllability subspace (c. s.) of the original pair (A, B). The family of c. s. of a fixed pair (A, B) is a subfamily, in gen-eral proper, of the (A, B)-invariant subspaces: the importance of c. s. derives from the fact that the restriction of A + BF to an (A +BF)-invariant c. s. can be assigned an arbitrary spectrum by suitable choice of F.
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Notes and References
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Wonham, W.M. (1974). Controllability Subspaces. In: Linear Multivariable Control. Lecture Notes in Economics and Mathematical Systems, vol 101. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-22673-5_6
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DOI: https://doi.org/10.1007/978-3-662-22673-5_6
Publisher Name: Springer, Berlin, Heidelberg
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