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Time scale modeling of dynamic networks with sparse and weak connections

  • Part II: Large Scale Systems
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Singular Perturbations and Asymptotic Analysis in Control Systems

Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 90))

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References

  1. Time-Scale Modeling of Dynamic Networks with Applications to Power Systems, J.H. Chow, Editor, Lecture Notes in Control and Information Sciences, Vol. 46, Springer-Verlag, Berlin, 1982.

    Google Scholar 

  2. P.V. Kokotovic, "Subsystems, Time Scales, and Multi-Modeling," Automatica, Vol. 17, pp. 789–795, 1981.

    Google Scholar 

  3. F. Delebecque and J.P. Quadrat, "Optimal Control of Markov Chains Admitting Strong and Weak Interactions." Automatica, Vol. 17, pp. 281–296, 1981.

    Google Scholar 

  4. R.G. Phillips and P.V. Kokotovic. "A Singular Perturbation Approach to Modeling and Control of Markov Chains." IEEE Transactions on Automatic Control, Vol. AC-26, pp. 1087–1094, 1982.

    Google Scholar 

  5. G. Peponides, P.V. Kokotovic and J.H. Chow, "Singular Perturbations and Time Scales in Nonlinear Models of Power Systems," IEEE Transactions on Circuits and Systems, Vol. CAS-29, pp. 758–767, 1982.

    Google Scholar 

  6. J.H. Chow, J. Cullum and R.A. Willoughby, "A Sparsity-Based Technique for Identifying Slow-Coherent Areas in Large Power Systems," IEEE Transactions on Power Apparatus and Systems, Vol. PAS-103, pp. 463–473, 1984.

    Google Scholar 

  7. D.M. Cvetkovic, M. Doob and H. Sachs, Spectra of Graphs — Theory and Application, VEB Deutscher Verlag der Wissenschaften, Berlin, 1982.

    Google Scholar 

  8. J.H. Chow and P.V. Kokotovic, "Sparsity and Time Scales." Proceedings of 1983 ACC, San Francisco, pp. 656–661.

    Google Scholar 

  9. P.V. Kokotovic, R.E. O'Malley, Jr. and P. Sannuti, "Singular Perturbations and Order Reduction in Control Theory — An Overview," Automatica, Vol. 12, pp. 123–132, 1976.

    Google Scholar 

  10. G.M. Peponides, "Nonexplicit Singular Perturbations and Interconnected Systems," Ph.D. Dissertation, Report R-960, Coordinated Science Laboratory, University of Illinois, Urbana, Illinois, 1982.

    Google Scholar 

  11. F. Delebecque, "A Reduction Process for Perturbed Markov Chains," SIAM J. Applied Mathematics, Vol. 43, pp. 325–350, 1983.

    Google Scholar 

  12. M. Coderch, A.S. Willsky, S.S. Sastry, D.A. Castanon, "Hierarchical Aggregation of Linear Systems with Multiple Time Scales," IEEE Transactions on Automatic Control, Vol. AC-28, pp. 1017–1030, 1983.

    Google Scholar 

  13. F.R. Gantmacher, The Theory of Matrices, Chelsea Publishing Company, New York, 1959.

    Google Scholar 

  14. R.L. Cresap and J.F. Hauer, "Emergence of a New Swing Mode in the Western Power System," IEEE Transactions on Power Apparatus and Systems, Vol. PAS-100, pp. 2037–2045, 1981.

    Google Scholar 

  15. EISPACK Guide — Matrix Eigensystem Routines, edited by B.T. Smith, et al., Springer-Verlag, New York, 1976.

    Google Scholar 

  16. J. Cullum and R.A. Willoughby. "Computing Eigenvalues of Very Large Symmetric Matrices," J. Computational Physics, Vol. 44, pp. 329–358, 1981.

    Google Scholar 

  17. H.A. Simons, "The Architecture of Complexity," Proceedings of the American Philosophical Society, Vol. 104, pp. 467–482, 1962.

    Google Scholar 

  18. R.M. May, Stability and Complexity in Model Ecosystems, Princeton University Press, 1973.

    Google Scholar 

  19. D.G. Feingold and R.S. Varga, "Block Diagonally Dominant Matrices and Generalizations of the Gerschgorin Circle Theorem," Pacific Journal of Mathematics, Vol. 12, pp. 1241–1250, 1962.

    Google Scholar 

  20. P.V. Kokotovic, "A Riccati Equation for Block-Diagonalization of Ill-Conditioned Systems," IEEE Transactions on Automatic Control, Vol. AC-20, pp. 812–814, 1975.

    Google Scholar 

  21. J.H. Chow, J.J. Allemong and P.V. Kokotovic, "Singular Perturbation Analysis of Systems with Sustained High Frequency Oscillations," Automatica, Vol. 14, pp. 271–279, 1978.

    Google Scholar 

  22. L.H. Fink, "Emergency Control Practices," Task Force on Emergency Control Report, Paper 85WM034-4, IEEE Winter Power Meeting, 1985.

    Google Scholar 

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Author information

Authors and Affiliations

  1. Electric Utility Systems Engineering Department, General Electric Company, 12345, Schenectady, NY

    J. H. Chow

  2. Coordinated Sciences Laboratory and Electrical Engineering Department, University of Illinois, 1101 W. Springfield Avenue, 61801, Urbana, IL

    P. V. Kokotovic

Authors
  1. J. H. Chow
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  2. P. V. Kokotovic
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Editor information

Petar V. Kokotovic Alain Bensoussan Gilmer L. Blankenship

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© 1987 Springer-Verlag

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Chow, J.H., Kokotovic, P.V. (1987). Time scale modeling of dynamic networks with sparse and weak connections. In: Kokotovic, P.V., Bensoussan, A., Blankenship, G.L. (eds) Singular Perturbations and Asymptotic Analysis in Control Systems. Lecture Notes in Control and Information Sciences, vol 90. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0007181

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  • DOI: https://doi.org/10.1007/BFb0007181

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-17362-5

  • Online ISBN: 978-3-540-47440-1

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