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Minimal positive realizations: a survey of recent results and open problems

Luca Benvenuti, Lorenzo Farina (2003)

Kybernetika

In this survey paper some recent results on the minimality problem for positive realizations are discussed. In particular, it is firstly shown, by means of some examples, that the minimal dimension of a positive realization of a given transfer function, may be much “larger” than its McMillan degree. Then, necessary and sufficient conditions for the minimality of a given positive realization in terms of positive factorization of the Hankel matrix are given. Finally, necessary and sufficient conditions...

Minimal realization for positive multivariable linear systems with delay

Tadeusz Kaczorek, Mikołaj Busłowicz (2004)

International Journal of Applied Mathematics and Computer Science

The realization problem for positive multivariable discrete-time systems with one time delay is formulated and solved. Conditions for the solvability of the realization problem are established. A procedure for the computation of a minimal positive realization of a proper rational matrix is presented and illustrated by an example.

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