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On positive reachability of time-variant linear systems on time scales

Bartosiewicz Z.

Bulletin of the Polish Academy of Sciences. Technical Sciences

2013

Vol. 61, nr 4

905--910

Positive reachability of time-variant linear positive systems on arbitrary time scales is studied. It is shown that the system is positively reachable if and only if a modified Gram matrix corresponding to the system is monomial. The general criterion is then specified for particular cases of continuous-time systems and various classes of discrete-time systems. It is shown that in the case of continuous-time systems with analytic coefficients the conditions for positive reachability are very restrictive, similarly as for time-invariant systems.

Time-variant Darlington synthesis and induced realizations

Pik D.

International Journal of Applied Mathematics and Computer Science

2001

Vol. 11, no 6

1331-1360

For a block lower triangular contraction T, necessary and sufficient conditions are given in order that there exist block lower triangular contractions T1,1, T2,1 and T2,2 such that Ut= [ T1,1 T ] T2,1 T2,2 is unitary. For the case when T1,1* and T2,2 have dense ranges, all such embeddings are described. Each unitary embedding of UT induces a contractive realization of T, and various properties of this realization are characterized in terms of the unitary embedding.