Scaling: a canonical design problem for networks

We motivate and address the optimal scaling problem, i.e. the problem of designing a diagonal matrix K so as to 1) place the eigenvalues of KG in the open right half plane and 2) optimize a scalar performance measure c(KG), for a given topology matrix G

[1]  C. Ballantine,et al.  Stabilization by a diagonal matrix , 1970 .

[2]  Fan Chung,et al.  Spectral Graph Theory , 1996 .

[3]  Stephen P. Boyd,et al.  Fast linear iterations for distributed averaging , 2003, 42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475).

[4]  E. Davison,et al.  On the stabilization of decentralized control systems , 1973 .

[5]  Sk Katti.  Decentralized control of linear multivariable systems , 1981 .

[6]  Richard M. Murray,et al.  INFORMATION FLOW AND COOPERATIVE CONTROL OF VEHICLE FORMATIONS , 2002 .

[7]  Daniel J. Stilwell,et al.  Communication, Feedback, and Decentralized Control , 2000 .

[8]  Jose C. Geromel,et al.  On the determination of a diagonal solution of the Lyapunov equation , 1985 .

[9]  Daniel Hershkowitz,et al.  Recent directions in matrix stability , 1992 .

[10]  A. S. Morse,et al.  Stabilization with decentralized feedback control , 1972, CDC 1972.

[11]  William B. Dunbar,et al.  Model predictive control of coordinated multi-vehicle formations , 2002, Proceedings of the 41st IEEE Conference on Decision and Control, 2002..

[12]  E. Yaz.  Linear Matrix Inequalities In System And Control Theory , 1998, Proceedings of the IEEE.

[13]  Daniel J. Stilwell,et al.  Communication, Feedback and Decentralized Control for Platoons of Underwater Vehicles , 2000 .

[14]  A. T. Fuller,et al.  On the stabilization of matrices and the convergence of linear iterative processes , 1958, Mathematical Proceedings of the Cambridge Philosophical Society.

[15]  Anne Greenbaum,et al.  Iterative methods for solving linear systems , 1997, Frontiers in applied mathematics.

[16]  Sandip Roy,et al.  A stochastic automaton-based algorithm for flexible and distributed network partitioning , 2005, Proceedings 2005 IEEE Swarm Intelligence Symposium, 2005. SIS 2005..

[17]  Daniel J. Stilwell,et al.  Platoons of underwater vehicles , 2000 .

[18]  A. Saberi,et al.  Some new results on stabilization by scaling , 2006, 2006 American Control Conference.

[19]  H. Khalil.  On the existence of positive diagonal P such that PA + A^{T}P l 0 , 1982 .

[20]  Stephen P. Boyd,et al.  Linear Matrix Inequalities in Systems and Control Theory , 1994 .