Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Concept Videos

Linear Approximation in Time Domain01:21

Linear Approximation in Time Domain

393
Nonlinear systems often require sophisticated approaches for accurate modeling and analysis, with state-space representation being particularly effective. This method is especially useful for systems where variables and parameters vary with time or operating conditions, such as in a simple pendulum or a translational mechanical system with nonlinear springs.
For a simple pendulum with a mass evenly distributed along its length and the center of mass located at half the pendulum's length,...
393
Linear time-invariant Systems01:23

Linear time-invariant Systems

1.0K
A system is linear if it displays the characteristics of homogeneity and additivity, together termed the superposition property. This principle is fundamental in all linear systems. Linear time-invariant (LTI) systems include systems with linear elements and constant parameters.
The input-output behavior of an LTI system can be fully defined by its response to an impulsive excitation at its input. Once this impulse response is known, the system's reaction to any other input can be...
1.0K
Gaussian Elimination: Problem Solving01:30

Gaussian Elimination: Problem Solving

266
Systems of linear equations in several variables are pivotal in modeling complex scenarios involving multiple unknowns and constraints. Such systems are widely used in various fields to represent relationships where several conditions must be simultaneously satisfied. Each variable in the system corresponds to an unknown quantity, while each equation imposes a linear constraint, leading to a structured approach for analyzing and solving real-world problems.A system of three equations with three...
266
Linearization and Approximation01:26

Linearization and Approximation

145
Linearization is a mathematical technique used to approximate complex, nonlinear functions with simpler linear models in the vicinity of a chosen reference point. The method is based on the idea that, although a function may be difficult to evaluate exactly, its behavior near a specific input value can often be closely approximated by the tangent line at that point. This approach is particularly useful when small deviations from a known value are involved.Consider the square root function, for...
145
Application of Linearization and Approximation01:29

Application of Linearization and Approximation

129
A drone flying through complex terrain often relies on more than one sensing method to estimate small changes in altitude. Along with direct measurements, air pressure provides a useful indirect indicator of vertical movement. Atmospheric pressure decreases as altitude increases, and this relationship is commonly described using an exponential model. Although accurate, converting pressure measurements into altitude values requires calculations that are too complex to perform repeatedly during...
129
Linear Approximation in Frequency Domain01:26

Linear Approximation in Frequency Domain

422
Linear systems are characterized by two main properties: superposition and homogeneity. Superposition allows the response to multiple inputs to be the sum of the responses to each individual input. Homogeneity ensures that scaling an input by a scalar results in the response being scaled by the same scalar.
In contrast, nonlinear systems do not inherently possess these properties. However, for small deviations around an operating point, a nonlinear system can often be approximated as linear....
422

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by
Same author

Gaussian-modulated continuous-variable quantum key distribution over 60 km fiber using an integrated silicon photonic receiver.

Optics letters·2026
Same author

Low-temperature plasma catalysis for VOCs control: Mechanistic insights and hybrid strategies.

Environmental research·2026
Same author

Dehydrocostus Lactone Suppresses Hepatocellular Carcinoma by Inhibiting Protein Tyrosine Kinase-7 Mediated β-Catenin Signaling.

Phytotherapy research : PTR·2026
Same author

FAIMS-IMS-QTOF MS Combined with TSPSO Deconvolution Algorithm for Effectively Probing Protein Conformation Changes Induced by Dipole Locking in FAIMS.

Analytical chemistry·2026
Same author

Multiple source enrichment model of organic matter in fifth member of Xujiahe Formation of Upper Triassic, northeastern Sichuan Basin.

Scientific reports·2026
Same author

Size-Matching-Driven SF<sub>6</sub> Capture Via Isoreticular Pore Contraction in a Microporous MOF.

Inorganic chemistry·2026

Related Experiment Video

Updated: Mar 19, 2026

Force and Position Control in Humans - The Role of Augmented Feedback
06:31

Force and Position Control in Humans - The Role of Augmented Feedback

Published on: June 19, 2016

8.3K

Geometric insight into linear augmented observers for uncertain systems.

Junhui Li1, Beili Gong1

  • 1School of Electrical Engineering, Guangxi University, Nanning, 530004, Guangxi, China.

ISA Transactions
|March 18, 2026
PubMed
Summary
This summary is machine-generated.

Linear augmented observers (LAOs) have structural limits impacting state and uncertainty estimation. This study reveals these limits depend on the nominal model

Keywords:
Estimation performanceGeometric approachLinear augmented observerNoise sensitivityObservabilityUncertain systems

More Related Videos

An Experimental Protocol for Assessing the Performance of New Ultrasound Probes Based on CMUT Technology in Application to Brain Imaging
16:01

An Experimental Protocol for Assessing the Performance of New Ultrasound Probes Based on CMUT Technology in Application to Brain Imaging

Published on: September 24, 2017

11.0K
Detection of Architectural Distortion in Prior Mammograms via Analysis of Oriented Patterns
13:44

Detection of Architectural Distortion in Prior Mammograms via Analysis of Oriented Patterns

Published on: August 30, 2013

43.8K

Related Experiment Videos

Last Updated: Mar 19, 2026

Force and Position Control in Humans - The Role of Augmented Feedback
06:31

Force and Position Control in Humans - The Role of Augmented Feedback

Published on: June 19, 2016

8.3K
An Experimental Protocol for Assessing the Performance of New Ultrasound Probes Based on CMUT Technology in Application to Brain Imaging
16:01

An Experimental Protocol for Assessing the Performance of New Ultrasound Probes Based on CMUT Technology in Application to Brain Imaging

Published on: September 24, 2017

11.0K
Detection of Architectural Distortion in Prior Mammograms via Analysis of Oriented Patterns
13:44

Detection of Architectural Distortion in Prior Mammograms via Analysis of Oriented Patterns

Published on: August 30, 2013

43.8K

Area of Science:

  • Control Systems Engineering
  • System Identification
  • Geometric Control Theory

Background:

  • Linear augmented observers (LAOs) are crucial for state and uncertainty estimation in control systems.
  • Current analyses of LAOs often assume a priori observability and overlook model structure impacts.
  • The inherent structural limitations of LAOs for uncertain systems remain incompletely understood.

Purpose of the Study:

  • To develop a geometric framework for characterizing the structural limitations of LAOs in uncertain linear systems.
  • To establish a precise condition for augmented system observability without prior assumptions.
  • To elucidate how nominal model structure dictates estimation error bounds and achievable accuracy.

Main Methods:

  • Development of a geometric framework to analyze LAO structural limitations.
  • Establishment of a necessary and sufficient condition for augmented system observability using invariant zeros.
  • Characterization of the estimation error subspace based on the nominal model's weakly unobservable subspace.

Main Results:

  • Observability of the augmented system is determined by the invariant zeros of the nominal model.
  • Estimation error is confined to a subspace dictated by the nominal model's structure.
  • Achieving arbitrarily small estimation error requires the nominal model to have no invariant zeros.
  • Quantification of measurement noise amplification with increasing observer bandwidth.

Conclusions:

  • The study provides explicit, verifiable structural criteria for assessing LAO feasibility and accuracy.
  • Invariant zeros of the nominal model fundamentally limit state and uncertainty estimation performance.
  • Understanding these structural limitations is key to designing effective LAOs for practical control systems.