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Inner algorithm test for controllability and observability

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1 Author(s)
Jury, E.I. ; University of California, Berkeley, CA, USA

In this note it is shown how the double triangularization algorithm developed for computing inners determinants can be adapted to test the controllability matrix ( B,AB,.., A^{n-1}B ) and observability matrix ( C^{T},A^{T}C^{T},...,(A^{T})^{n-1}C^{T} ) to have rank of " n ." The controllability and observability conditions are shown to be equivalent to n^{2} \times n(n + l - 1 ) and n(n + l' - 1) \times n^{2} innerwise matrices to be nonsingular (i.e., to have a rank n2).

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Automatic Control, IEEE Transactions on  (Volume:18 ,  Issue: 6 )