Inner algorithm test for controllability and observability
E.I. Jury · IEEE Transactions on Automatic Control · 1973
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 ton^{2} \times n(n + l - 1) andn(n + l' - 1) \times n^{2}innerwise matrices to be nonsingular (i.e., to have a rank n2).