Optimal H&lt;inf&gt;i&lt;/inf&gt;=H&lt;inf&gt;&amp;#x221E;&lt;/inf&gt; fault detection filter design: An iterative LMI approach

Li, W.; Ding, Steven X.; Zhu, Zhencai

doi:10.1109/cdc.2009.5399722

Cited by 2 publications

(3 citation statements)

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“…The FD over the EIA is elaborated on in [6, section 7.8.4], [3, section 8.4], [1,11,12,19,20] and [21], where the Kalman-Yakubovič-Popov (KYP) lemma is applied, and over a frequency region in [2,5], where the generalized KYP lemma is applied. The FD over the EIA is elaborated on in [6, section 7.8.4], [3, section 8.4], [1,11,12,19,20] and [21], where the Kalman-Yakubovič-Popov (KYP) lemma is applied, and over a frequency region in [2,5], where the generalized KYP lemma is applied.…”

Section: Introductionmentioning

confidence: 99%

“…The first one is based on considering the FD filter in an observer form, and formulating bilinear matrix inequalities in unknown matrices. The FD over the EIA is elaborated on in [, section 7.8.4], [, section 8.4], and , where the Kalman‐Yakubovič‐Popov (KYP) lemma is applied, and over a frequency region in , where the generalized KYP lemma is applied. See section 7.8.4 of for a review of the problem over the entire EIA, and section 7.8.5 of for the problem over a frequency region.…”

Section: Introductionmentioning

confidence: 99%

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New Condition for FD, All Filters, and New KYP Lemma

Stefanovski¹

2017

Asian Journal of Control

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This paper presents a necessary and sufficient condition for the ℋ − ∕ℋ ∞ fault detection (FD) problem, under a quite general and natural assumption. The condition is actually a constant inertia on the extended imaginary axis (EIA) of a para-hermitian rational matrix (RM). An observer solution is given. Another two main results are the presentation of all problem solutions, and a necessary and sufficient condition for constant inertia on the EIA or in a given frequency region, for a class of para-hermitian RMs, in terms of linear matrix inequalities. The latter result can be regarded as a generalization of the Kalman-Yakubovich-Popov (KYP) lemma. Key Words:Fault detection in presence of disturbances, J-spectral factorization, inertia of hermitian matrix, finite and infinite zeros.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

New Condition for FD, All Filters, and New KYP Lemma

Stefanovski¹

2017

Asian Journal of Control

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“…The unified solutions are obtained by solving Riccati equations, and they deliver FDFs that can achieve an optimal trade-off between the robustness against disturbances and the sensitivity to system faults in the whole residual subspace and over the whole frequency [2]. In [20], an LMI approach for optimal H i /H ∞ FDF design has been presented for linear time-invariant (LTI) systems. However, these papers considered only unknown inputs in the FDF design.…”

Section: Introductionmentioning

confidence: 99%

Optimal H _i / H _∞ fault‐detection filter design for uncertain linear time‐invariant systems: an iterative linear matrix inequality approach

Zhu

Zhou

et al. 2013

IET Control Theory & Applications

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An iterative linear matrix inequality (LMI) approach is proposed to design fault-detection filters (FDFs) of uncertain linear time-invariant (LTI) systems. The obtained FDF is the optimal solution for the H i /H ∞ (with H ∞ /H ∞ and H − /H ∞ being two extreme cases) optimisation problem of FDF design and can achieve the best trade-off between robustness against unknown disturbances and sensitivity to system faults. The authors first derive the theoretical optimal H i /H ∞ FDFs for uncertain LTI systems based on the co-inner-outer factorisation technique. Then a new optimisation problem is formulated to obtain the optimal FDFs that can approach the theoretical optimal ones as much as possible. An iterative LMI approach is presented to find the solution in the state-space form. The effectiveness of the proposed approach is illustrated by a numerical example.

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Optimal H<inf>i</inf>=H<inf>∞</inf> fault detection filter design: An iterative LMI approach

Cited by 2 publications

References 20 publications

New Condition for FD, All Filters, and New KYP Lemma

New Condition for FD, All Filters, and New KYP Lemma

Optimal H _i / H _∞ fault‐detection filter design for uncertain linear time‐invariant systems: an iterative linear matrix inequality approach

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Optimal H<inf>i</inf>=H<inf>&#x221E;</inf> fault detection filter design: An iterative LMI approach

Cited by 2 publications

References 20 publications

New Condition for FD, All Filters, and New KYP Lemma

New Condition for FD, All Filters, and New KYP Lemma

Optimal H i / H ∞ fault‐detection filter design for uncertain linear time‐invariant systems: an iterative linear matrix inequality approach

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Optimal H<inf>i</inf>=H<inf>∞</inf> fault detection filter design: An iterative LMI approach

Optimal H _i / H _∞ fault‐detection filter design for uncertain linear time‐invariant systems: an iterative linear matrix inequality approach