Controllability-observability of expanded composite systems.

*(English)*Zbl 1031.93006As is known, the Inclusion Principle developed by Šiljak and co-workers [see e.g. D. D. Šiljak, Decentalized control of complex systems, Springer, New York (1999; Zbl 0728.93004)] enables a framework to be defined for dealing with dynamic systems with different dimensions so that both systems are related through linear transformations (expansions and contractions), taking the freedom of the selection of the so-called complementary matrices.

In this respect, the main contribution of the paper under review is proving that an expanded system can always preserve controllability-observability of both the subsystems and the overall system provided that both properties hold for the original system when considering a disjoint structure of its subsystems. These results are stated and proved in Theorems 6 and 7 (concerning subsystems) and Theorem 8 (for the overall expanded composite system), where an appropriate choice of the complementary matrices satisfying “controllability-observability” is guaranteed.

In this respect, the main contribution of the paper under review is proving that an expanded system can always preserve controllability-observability of both the subsystems and the overall system provided that both properties hold for the original system when considering a disjoint structure of its subsystems. These results are stated and proved in Theorems 6 and 7 (concerning subsystems) and Theorem 8 (for the overall expanded composite system), where an appropriate choice of the complementary matrices satisfying “controllability-observability” is guaranteed.

Reviewer: Pablo Gonzales-Vera (La Laguna)

##### Keywords:

decentralized control; inclusion principle; transformations; complementary matrices; expanded system; controllability-observability; subsystems; composite system
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\textit{L. Bakule} et al., Linear Algebra Appl. 332--334, 381--400 (2001; Zbl 1031.93006)

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##### References:

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