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Mathematical Tools

  • Magdi S. Mahmoud

Abstract

The backbone of this chapter evolves from finite dimension vector spaces, mappings and convex analysis. Much of the material is standard linear algebra, with which the reader is assumed to have some familiarity and therefore our intention is to provide an overview of the key ideas and tools.

Keywords

Vector Space Lyapunov Function Singular Value Decomposition Matrix Function Null Space 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. 1.
    Apostol, T. M., Mathematical Analysis. Addison-Wesley, Reading, 1957. MATHGoogle Scholar
  2. 2.
    Boyd, S., L. El Ghaoui, E. Feron and V. Balakrishnan, Linear Matrix Inequalities in Systems and Control Theory, SIAM Studies in Applied Mathematics, SIAM, Philadelphia, 1994. CrossRefGoogle Scholar
  3. 3.
    Fridman E. and U. Shaked, “Delay-Dependent Stability and \({\mathcal{H}}_{\infty}\) Control: Constant and Time-Varying Delays”, Int. J. Control, vol. 76, 2003, pp. 48–60. MathSciNetMATHCrossRefGoogle Scholar
  4. 4.
    Gu, K., V. L. Kharitonov, Jie Chen, Stability of Time-Delay Systems, Birkhäuser, Boston, 2003. MATHCrossRefGoogle Scholar
  5. 5.
    Guo, Y., D. J. Hill and Y. Wang, “Nonlinear Decentralized Control of Large-Scale Power Systems”, Automatica, vol. 36, 2000, pp. 1275–1289. MathSciNetMATHCrossRefGoogle Scholar
  6. 6.
    Hale, J. K. and S. M. Verduyn Lunel, Introduction to Functional Differential Equations, Springer, Berlin, 1993. MATHGoogle Scholar
  7. 7.
    Kailath T., Linear Systems, Prentice-Hall, New York, 1980. MATHGoogle Scholar
  8. 8.
    Khalil, H. K., Nonlinear Systems (2nd ed.), Prentice-Hall, New York, 2002. MATHGoogle Scholar
  9. 9.
    Mahmoud, M. S., Robust Control and Filtering for Time-Delay Systems, Dekker, New York, 2000. Google Scholar
  10. 10.
    Petersen I. R., Syst. Control Lett., vol. 8, 1987, pp. 351–357. MATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag London Limited 2011

Authors and Affiliations

  1. 1.Department of Systems EngineeringKing Fahd Univ. of Petroleum & MineralsDhahranSaudi Arabia

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