Reachability, observability and strict equivalence of networks of linear systems

Mathematics of Control, Signals, and Systems

Volumn 25, Issue 4, 2013, Pages 437-471

  Fuhrmann, Paul A ^a   Helmke, Uwe ^b  

^a BEN GURION UNIVERSITY OF THE NEGEV   (Israel)

^b UNIVERSITY OF WÜRZBURG   (Germany)

Author keywords

Interconnections; Linear systems; Networks; Observability; Reachability; System equivalence

Indexed keywords

HOMOGENEOUS NETWORK; INTERCONNECTIONS; LINEAR MIMO SYSTEMS; REACHABILITY; SISO SYSTEMS; STRICT EQUIVALENCE; SYSTEM EQUIVALENCE;

COMPLEX NETWORKS; EQUIVALENCE CLASSES; HETEROGENEOUS NETWORKS; LINEAR SYSTEMS; MIMO SYSTEMS; NETWORKS (CIRCUITS);

OBSERVABILITY;

EID: 84880729807     PISSN: 09324194     EISSN: 1435568X     Source Type: Journal    
DOI: 10.1007/s00498-012-0104-0     Document Type: Article

References (17)

1. Bamieh B, Paganini F, Dahleh MA (2002) Distributed control of spatially invariant systems. IEEE Trans Autom Control 47:1091-1107
2. Brockett RW (2010) On the control of a flock by a leader. In: Proceedings of the Steklov Institute of Mathematics, vol 268, pp 49-57
3. Callier FM, Nahum CD (1975) Necessary and sufficient conditions for the complete controllability and observability of systems in series using the coprime decomposition of a rational matrix. IEEE Trans Circuits Syst 22:90-95
4. Fuhrmann PA (1975) On controllability and observability of systems connected in parallel. IEEE Trans Circuits Syst 22:57
5. Fuhrmann PA (1976) Algebraic system theory: an analyst's point of view. J Franklin Inst 301:521-540
6. Fuhrmann PA (1977) On strict system equivalence and similarity. Int J Contr 25:5-10
7. Hara S, Hayakawa T, Sugata H (2009) LTI systems with generalized frequency variables: a unified framework for homogeneous multi-agent dynamical systems. SICE J Control Meas Syst Integr 2:299-306
8. Leonard NE, Krishnaprasad PS (1994) Control of switched electrical networks using averaging on Lie groups. In: Proceedings of the 33rd IEEE Conference Decision and Control, pp 1919-1924
9. Levy B, Kung SY, Morf M, Kailath T (1977) A unification of system equivalence definitions. In: Proceedings of the IEEE Conference Decision and Control, pp 795-800
10. Li J-S, Khaneja N ((2006)) Control of inhomogeneous quantum ensembles. Phys Rev A 73:030302
11. Parlangeli G, Notarstefano G (2012) On the reachability and observability of path and cycle graphs. IEEE Trans Autom Control 57:743-748
12. Pugh AC, Shelton AK (1978) On a new definition of strict equivalence. Int J Contr 27:657-672
13. Rosenbrock HH (1970) State-space and multivariable theory. Wiley, New York
14. Rosenbrock HH, Pugh AC (1974) Contributions to a hierarchical theory of systems. Int J Control 19:845-867
15. Schumacher JM (1988) Transformations of linear systems under external equivalence. Linear Algebra Appl 102:1-33
16. Siljak DD (1991) Decentralized control of complex systems. In: Mathematics in science and engineering, vol 184. Academic Press, San Diego
17. Smith MC (1981) Matrix fractions and strict system equivalence. Int J Control 34:869-883