Observability Through a Matrix-Weighted Graph

Creative Commons License

TUNA S. E.

IEEE TRANSACTIONS ON AUTOMATIC CONTROL, cilt.63, sa.7, ss.2061-2074, 2018 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 63 Sayı: 7
  • Basım Tarihi: 2018
  • Doi Numarası: 10.1109/tac.2017.2758172
  • Dergi Adı: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.2061-2074
  • Anahtar Kelimeler: Connectivity, effective conductance, matrix-weighted graph, observability, synchronization, MULTIAGENT SYSTEMS, RELATIVE MEASUREMENTS, LINEAR-SYSTEMS, SYNCHRONIZATION, NETWORKS, CONSENSUS, CONTROLLABILITY, RESISTANCE, DESIGN
  • Orta Doğu Teknik Üniversitesi Adresli: Evet

Özet

Observability of an array of identical linear time-invariant systems with incommensurable output matrices is studied, where an array is called observable when identically zero relative outputs imply synchronized solutions for the individual systems. It is shown that the observability of an array is equivalent to the connectivity of its interconnection graph, whose edges are assigned matrix weights. Moreover, to better understand the relative behavior of distant units, pairwise observability that concerns with the synchronization of a certain pair of individual systems in the array is studied. This milder version of observability is shown to be closely related to certain connectivity properties of the interconnection graph as well. Pairwise observability is also analyzed using the circuit theoretic tool effective conductance. The observability of a certain pair of units is proved to be equivalent to the nonsingularity of the (matrix-valued) effective conductance between the associated pair of nodes of a resistive network (with matrix-valued parameters) whose node admittancematrix is the Laplacian of the array's interconnection graph.