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Stability

Stability

The time response of a linear time-invariant (LTI) system can be divided into transient and steady-state responses. The transient response represents the system's initial reaction to a change in input and diminishes to zero over time. In contrast, the steady-state response is the behavior that persists after the transient effects have faded.
The stability of an LTI system is determined by the roots of its characteristic equation, known as poles. A system is stable if it produces a bounded...

Pole and System Stability

Pole and System Stability

The transfer function is a fundamental concept representing the ratio of two polynomials. The numerator and denominator encapsulate the system's dynamics. The zeros and poles of this transfer function are critical in determining the system's behavior and stability.
Simple poles are unique roots of the denominator polynomial. Each simple pole corresponds to a distinct solution to the system's characteristic equation, typically resulting in exponential decay terms in the system's response.

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Related Experiment Video

Updated: Jul 7, 2026

Evaluating Postural Control and Lower-extremity Muscle Activation in Individuals with Chronic Ankle Instability

Evaluating Postural Control and Lower-extremity Muscle Activation in Individuals with Chronic Ankle Instability

Published on: September 18, 2020

Process stationarity and reliability of trunk postural stability.

HyunWook Lee¹, Kevin P Granata

¹School of Biomedical Engineering and Sciences, Virginia Polytechnic Institute and State University, 219 Norris Hall (0219), Blacksburg, VA 24061, USA. hwlee@vt.edu

Clinical Biomechanics (Bristol, Avon)

|February 29, 2008

Summary

Torso stability assessment requires at least 30 seconds of data for reliable results. Nonlinear measures offer excellent reliability for seated balance tasks, particularly for inter-session comparisons.

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Area of Science:

Biomechanics
Human Movement Science
Motor Control

Background:

Assessing torso stability is crucial for understanding seated balance.
Current methods rely on postural variability and nonlinear analyses but need sufficient duration and reliability.
This study aimed to determine the necessary trial duration and reliability of torso stability assessment.

Purpose of the Study:

To establish the minimum trial duration for reliable torso stability assessment.
To characterize the test-retest reliability of different torso stability measures.
To identify optimal methods for seated balance analysis.

Main Methods:

Recorded kinetic and kinematic data during seated balance on a wobbly seat pan.
Evaluated stability using dynamic variability and nonlinear analyses.
Determined minimum trial duration via process stationarity and measured reliability using intra-class correlations.

Main Results:

A trial duration of 30.2 seconds was necessary for process stationarity.
Multi-dimensional movement measures achieved stationarity faster.
Movement variability showed moderate intra-session (ICC=0.64) and inter-session (ICC=0.42) reliability.
Nonlinear measures, such as H(S) and Lyapunov exponents, demonstrated excellent inter-session reliability (up to ICC=0.83).

Conclusions:

A minimum trial duration of 30 seconds is recommended for torso stability assessments.
Intra-session reliability is moderate to excellent, but inter-session comparisons require more measurements.
Nonlinear measures like H(S) and Lyapunov exponents are superior for both intra- and inter-session torso stability analysis.