Abstract
This paper aims at a better understanding of reachability and observability properties of heterogeneous networks of linear systems. It extends prior work by Hara et al. (SICE J Control Meas Syst Integr 2:299–306, 2009), who characterized reachability for homogeneous networks of identical linear SISO systems. Our approach is based on extending the classical notion of strict system equivalence to networks of linear systems. We survey and extend known characterizations for reachability and observability for arbitrary interconnected linear MIMO systems. Both static and dynamic interconnection laws are considered, and various applications to classes of homogeneous and heterogeneous networks are derived.
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Acknowledgments
Support of U. Helmke by a grant HE 1858/12-2 within the German Research Foundation DFG programme SPP 1305 is gratefully acknowledged. A preliminary version of Theorem 4.1 has been derived earlier in collaboration with Jens Jordan.
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Dedicated to the memory of H. H. Rosenbrock, a great pioneer of system theory.
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Fuhrmann, P.A., Helmke, U. Reachability, observability and strict equivalence of networks of linear systems. Math. Control Signals Syst. 25, 437–471 (2013). https://doi.org/10.1007/s00498-012-0104-0
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DOI: https://doi.org/10.1007/s00498-012-0104-0