“On the Use of a Block Analog of the Gerschgorin Circle-Theorem in the Design of Decentralized Control of a Class of Large-Scale Systems”

Authors: Ole A. Solheim,
Affiliation: NTNU, Department of Engineering Cybernetics
Reference: 1981, Vol 2, No 2, pp. 107-118.

Keywords: Decentralized control, decentralized estimation, eigenvalues, stability, the block Gerschgorin theorem

Abstract: The paper deals with the design of decentralized control of interconnected dynamic systems. It is assumed that each subsystem has its own control input and that the interconnections are through the states of the other subsystems. The purpose of the present paper is to investigate the possibility of using the so-called block Gerschgorin theorem to evaluate the stability of the total system, given the local controllers. This theorem enables us to determine inclusion regions for the eigenvalues of the total system and these regions are usually sharper than those obtained by the usual Gerschgorin circle theorem.

PDF PDF (1944 Kb)        DOI: 10.4173/mic.1981.2.5

DOI forward links to this article:
[1] Ole A. Solheim (1983), doi:10.4173/mic.1983.4.3
[2] O. Egeland (1986), doi:10.1109/ROBOT.1986.1087605
[3] O. Touhami and M. Ferhi-Hamis (2006), doi:10.1109/SSST.2006.1619077
[4] M.K. Sundareshan and R.M. Elbanna (1991), doi:10.1109/9.85064
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  title={{On the Use of a Block Analog of the Gerschgorin Circle-Theorem in the Design of Decentralized Control of a Class of Large-Scale Systems}},
  author={Solheim, Ole A.},
  journal={Modeling, Identification and Control},
  publisher={Norwegian Society of Automatic Control}