Stabilization Method Irrespective of Bounds of Uncertain Variations

  Since most systems often have inherent uncertainties, a stabilization method should be developed for a system model that contains uncertain parameters. In most instances, physical, chemical, biological, and economical phenomena depend naturally not only on the present state but also on past occurrences. The importance of time delays in the stability analysis is well recognized in a wide range of applications. Therefore, we consider the stabilization problem of a class of uncertain delay systems.
  It is useful to classify the existing results on the robust control problem of uncertain systems into two categories. The first category includes several results that provide conditions depending on the bounds of uncertain parameters. On the other hand, the second category includes results that provide conditions that are independent of the bounds of uncertain parameters but dependent on their locations in system matrices. In this study, we specifically address the second category.
  The stabilizability conditions in the second category can be verified simply by examining the positions of uncertain entries in given system matrices. Once a system satisfies the stabilizability conditions, a stabilizing controller can be constructed, however large the given bounds of uncertain variations might be. We can redesign the controller to improve robustness simply by modifying the design parameter when the uncertain parameters exceed the upper bounds given beforehand.

  This research is partially supported by Japan Society for the Promotion of Science, Grant-in-Aid for Young Scientists (Start-up), 20860040.

  • Tomoaki HASHIMOTO and Takashi AMEMIYA:
    Controllability and Observability of Linear Time-Invariant Uncertain Systems Irrespective of Bounds of Uncertain Parameters,
    IEEE Transactions on Automatic Control,
    Vol.56, No.8, pp.1807-1817, 2011. (DOI: 10.1109/TAC.2010.2096013)
  • Tomoaki HASHIMOTO and Takashi AMEMIYA:
    Stabilization of Linear Time-varying Uncertain Delay Systems with Double Triangular Configuration,
    WSEAS Transactions on Systems and Control,
    Vol.4, No.9, pp.465-475, 2009.
  • Tomoaki HASHIMOTO and Takashi AMEMIYA:
    Output Feedback Stabilization of Linear Time-varying Uncertain Delay Systems,
    Mathematical Problems in Engineering,
    Vol.2009, Article ID 457468, 2009. (DOI: 10.1155/2009/457468)
  • Tomoaki HASHIMOTO, Takashi AMEMIYA and Hironori A. FUJII:
    Stabilization of Linear Uncertain Delay Systems with Antisymmetric Stepwise Configurations,
    Journal of Dynamical and Control Systems,
    Vol.14, No.1, pp.1-31, 2008. (DOI: 10.1007/s10883-007-9035-3)