Related Experiment Video
Updated: Aug 11, 2026

Sit-to-stand-and-walk from 120% Knee Height: A Novel Approach to Assess Dynamic Postural Control Independent of Lead-limb
Published on: August 30, 2016
Straight-line stabilization
1Department of Mathematics, Hong Kong University of Science and Technology, Hong Kong.
Abstract:
For finite-dimensional maps, an unstable orbit in a neighborhood of an unstable fixed point can be stabilized by adjusting parameters so that the orbit goes to the fixed point along the straight line connecting the orbit (at a given time) and the fixed point [Yang Ling, Liu Zengrong and Jian-min Mao, Phys. Rev. Lett. 84, 67 (2000)]. This is called straight-line stabilization. In this paper, we derive the expression for the region of stabilization, i.e., the region within which the straight-line stabilization method is valid. For two-dimensional maps, the parameter adjustments needed by the stabilization method are explicitly given for nine cases. Stabilization of unstable flows, with or without introducing a Poincare map, is also investigated.
More Related Videos
Related Concept Videos
Stability of structures
Pole and System 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.
Linear Approximation in Time Domain
For a simple pendulum with a mass evenly distributed along its length and the center of mass located at half the pendulum's length, the...
Stability
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...
Linearization and Approximation
Application of Linearization and Approximation

