Nonstandard Extension of H-Optimal Control for Singularly Perturbed Systems

  • Hua Xu
  • Koichi Mizukami
Part of the Annals of the International Society of Dynamic Games book series (AISDG, volume 5)


In this paper, we consider a nonstandard extension of the H -optimal control problem for singularly perturbed systems and relax the nonsingularity conditions made in the paper of Pan and Başar [11] We prove that all the results concerning the composite controller in the paper above still hold true even if the system is a nonstandard singularly perturbed system. We show that the composite optimal controller, which guarantees a disturbance attenuation level larger than the upper bound of the full-order system when ε is sufficiently small, can be constructed very simply by only revising a slow controller. This paper also provides a concise procedure to construct the composite controller. Some numerical examples, which can not be solved using the method of the above paper, are presented to illustrate the theoretical results.


Algebraic Riccati Equation Disturbance Attenuation Fast Subsystem Slow Subsystem Perturb System 
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Copyright information

© Springer Science+Business Media New York 2000

Authors and Affiliations

  • Hua Xu
    • 1
  • Koichi Mizukami
    • 2
  1. 1.Graduate School of Systems ManagementThe University of TsukubaTokyoJapan
  2. 2.Faculty of Integrated Arts and SciencesHiroshima UniversityHigashi-HiroshimaJapan

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