Principal Component Analysis in Linear Systems¶
Moore, B. C. (1981). Principal Component Analysis in Linear Systems: Controllability, Observability, and Model Reduction. IEEE Transactions on Automatic Control, 26(1), 17-32.
Cited by¶
5 citations across 5 artifacts.
Each citation links to the sentence it supports in the citing article.
Primes¶
- Controllability
- Variants include: structural controllability (generic controllability based on system-matrix sparsity pattern, independent of parameter values); small-time local controllability (controllability within a neighborhood, possibly within a short horizon); robust controllability (preserved under model uncertainty); constrained controllability (controllability when inputs are restricted to a subset — e.g., bounded thrust); controllability gramian (quantifies how controllable each state direction is, supporting model reduction and actuator placement)
This sourceIntroduces balanced realizations and the use of controllability/observability gramians to quantify how controllable each state direction is, supporting model reduction.
Supported in partVerified against the publisher's abstract
Abstract backs controllability-subspace analysis for model reduction, but not the gramian's per-direction quantification, actuator placement, or the other listed variants.
“For asymptotically stable systems, this yields working approximations ofX_{c}, X_{\bar{o}}, the controllable and unobservable subspaces. It is proposed that a natural first step in model reduction is to apply the mechanics of minimal realization using these working subspaces.”
- Variants include: structural controllability (generic controllability based on system-matrix sparsity pattern, independent of parameter values); small-time local controllability (controllability within a neighborhood, possibly within a short horizon); robust controllability (preserved under model uncertainty); constrained controllability (controllability when inputs are restricted to a subset — e.g., bounded thrust); controllability gramian (quantifies how controllable each state direction is, supporting model reduction and actuator placement)
- Linearity
- Listed in the references but not attached to a specific claim.
- Measurement Uncertainty and Observational Noise
- Listed in the references but not attached to a specific claim.
- Observability
- Variants include: structural observability (generic observability based on the sparsity pattern of system matrices, independent of parameter values); weak vs. strong observability (minimum-interval length for state reconstruction); robust observability (preserved under model uncertainty and disturbances); observability gramian (quantifies how observable each state direction is, enabling model reduction by truncating poorly-observable modes)
Supported in partVerified against the publisher's abstract
Abstract supports observability and balanced model reduction, but names none of the four variants (structural, weak/strong, robust, gramian) the claim lists.
“It is proposed that a natural first step in model reduction is to apply the mechanics of minimal realization using these working subspaces.”
- Variants include: structural observability (generic observability based on the sparsity pattern of system matrices, independent of parameter values); weak vs. strong observability (minimum-interval length for state reconstruction); robust observability (preserved under model uncertainty and disturbances); observability gramian (quantifies how observable each state direction is, enabling model reduction by truncating poorly-observable modes)
- Predictive Coding
- Listed in the references but not attached to a specific claim.
Verification¶
Does it exist? Confirmed. This work's DOI resolves to a registered record, which fixes its identity. That is all it fixes.
Does it back the claim? Read against the text for 2 of 5 citations: 2 supported in part. Each verdict is shown under its citation below, with what in the work backs the sentence.
Support is checked per citation rather than per work — the same source can be cited soundly in one article and wrongly in another. Per-citation recording began recently, so a citation with no recorded check is a gap in the record rather than evidence it went unchecked.
See how references were verified.
Registry ID ref:593f6a942f54 · see in the full table