Linear Stochastic Systems by Anders Lindquist & Giorgio Picci

Author:Anders Lindquist & Giorgio Picci
Language: eng
Format: epub
Publisher: Springer Berlin Heidelberg, Berlin, Heidelberg

(10.11)

where T 1, is an n × n nonsingular matrix and T 2 is a p × p orthogonal matrix. Clearly, the state space X, defined by (10.8), is an invariant of this equivalence, and we shall look for conditions under which this invariant is complete in the sense that there is bijective correspondence between equivalence classes and spaces X. Since realizations and such that give rise to the same X, an obvious necessary condition is that

(10.12)

Moreover, as pointed out above, it is necessary to consider only models for which

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