Zeros in Discrete-Time Mimo Lti Systems and the Output-Zeroing Problem

Tokarzewski, J.

International Journal of Applied Mathematics and Computer Science, Tome 10 (2000) no. 3, pp. 537-557.

Résumé

A geometric interpretation of invariant zeros of MIMO LTI discrete-time systems is provided. The zeros are treated as the triples: complex number, state zero direction, input zero direction. Such a treatment is strictly connected with the output zeroing problem and in that spirit the zeros can be easily interpreted even in the degenerate case (i.e. when each complex number constitutes an invariant zero). Simply, in the degenerate case, to each complex number we can assign an appropriate real initial condition and an appropriate real input sequence which produce a non-trivial solution to the state equation and a zero system response. Clearly, when zeros are treated merely as complex numbers, such an interpretation is impossible. The proposed definition of invariant zeros is compared with other commonly known definitions. It is shown that each Smith zero of the system matrix is also an invariant zero in the sense of the definition adopted in the paper. On the other hand, simple numerical examples show that the considered definition of invariant zeros and the Davison-Wang definition are not comparable. The output-zeroing problem for systems decouplable by state feedback is also described.

Détail

Keywords: linear multivariable systems, discrete-time systems, invariant zeros, Davison-Wang definition, output-zeroing problem
Mots-clés : wielowymiarowy układ liniowy, system dyskretny