Abstract :
The problem of determining system zeros (transmission+decoupling) of a linear system S(A, B, C, D) employing the canonical decomposition theorem is discussed. The zeros are characterized as eigenvalues of an appropriate real matrix of order of the state matrix. When the system is transformed to the Kalman canonical form that matrix takes an upper-triangular block form consistent with the Kalman structure of the state matrix. The submatrices of the diagonal describe successively output decoupling, transmission, input-output decoupling and input decoupling zeros. A suitable procedure for the computation of the zeros is proposed. As is shown, each system S(A, B, C, D) may be diagonally decoupled by state feedback and squaring down. The presented approach is based on the Moore-Penrose pseudoinverse of the first nonzero Markov parameter.
Keywords :
MIMO systems; Markov processes; eigenvalues and eigenfunctions; linear systems; matrix algebra; state feedback; Kalman canonical form; MIMO LTI system; Markov parameter; Moore-Penrose pseudoinverse; canonical decomposition theorem; linear system; state feedback; state matrix eigenvalue; system zero; Eigenvalues and eigenfunctions; Filtering theory; Kalman filters; Markov processes; Matrix decomposition; Skeleton; State feedback; Linear systems; decoupling zeros; invariant zeros; state-space methods; transmission zeros;
