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 as. of a fixed pair (A, B) is a subfamily, in general proper, of the (A, B)-mvariant 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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© 1979 Springer-Verlag New York
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Wonham, W.M. (1979). Controllability Subspaces. In: Linear Multivariable Control: a Geometric Approach. Applications of Mathematics, vol 10. Springer, New York, NY. https://doi.org/10.1007/978-1-4684-0068-7_6
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DOI: https://doi.org/10.1007/978-1-4684-0068-7_6
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4684-0070-0
Online ISBN: 978-1-4684-0068-7
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