• Title/Summary/Keyword: indefinite quadratic form

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Robust Kalman Filter Design in Indefinite inner product space (부정내적공간에서의 강인칼만필터 설계)

  • Lee, Tae-Hoon;Yoon, Tae-Sung;Park, Jin-Bae
    • Proceedings of the KIEE Conference
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    • 2002.11c
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    • pp.104-109
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    • 2002
  • A new robust Kalman filter is designed for the linear discrete-time system with norm-bounded parametric uncertainties. Sum quadratic constraint, which describes the uncertainties of the system, is converted into an indefinite quadratic form to be minimized in indefinite inner product space. This minimization problem is solved by the new robust Kalman filter. Since the new filter is obtained by simply modifying the conventional Kalman filter, robust filtering scheme can be more readily designed using the proposed method in comparison with the existing robust Kalman filters. A numerical example demonstrates the robustness and the improvement of the proposed filter compared with the existing filters.

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Discrete-Time Robust $H_{\infty}$ Filter Design via Krein Space

  • Lee, T.H.;Jung, S.Y.;Seo, J.E.;Shin, D.H.;Park, J.B.
    • 제어로봇시스템학회:학술대회논문집
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    • 2003.10a
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    • pp.542-547
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    • 2003
  • A new approach to design of a discrete-time robust $H_{\infty}$ filter in finite horizon case is proposed. It is shown that robust $H_{\infty}$ filtering problem can be cast into the minimization problem of an indefinite quadratic form, which can be solved by implementing the Kalman filter defined in Krein space. The proposed filter is readily derived by simply augmenting the state space model and has the robustness property against the parameter uncertainties of a given system.

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Conditional Feynman Integrals involving indefinite quadratic form

  • Chung, Dong-Myung;Kang, Si-Ho
    • Journal of the Korean Mathematical Society
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    • v.31 no.3
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    • pp.521-537
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    • 1994
  • We consider the Schrodinger equation of quantum mechanics $$ i\hbar\frac{\partial t}{\partial}\Gamma(t, \vec{\eta}) = -\frac{2m}{\hbar}\Delta(t, \vec{\eta}) + V(\vec{\eta}\Gamma(t, \vec{\eta}) (1.1) $$ $$ \Gamma(0, \vec{\eta}) = \psi(\vec{\eta}), \vec{\eta} \in R^n $$ where $\Delta$ is the Laplacian on $R^n$, $\hbar$ is Plank's constant and V is a suitable potential.

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