An Algorithm for Computing Invariant Zeros in Discrete-time Proper Systems

J. Tokarzewski, L. Sokalski, and A. Muszynski (Poland)


Control, Linear Discrete-Time Systems, Invariant Zeros


An algorithm for computing invariant zeros of a MIMO LTI proper discrete-time system S(A,B,C,D) is provided in the paper. Nothing is assumed about the relationship of the number of inputs to the number of outputs nor about the normal rank of the underlying system matrix. The zeros are treated as the triples: complex number, nonzero state-zero direction, input-zero direction. The proposed algorithm is based on singular value decomposition (SVD) of the first nonzero Markov parameter and enables us to find all invariant zeros in at most finite number of steps. The presented results are illustrated by simple numerical examples.

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