Recent trends in the stability analysis of hybrid dynamical systems

1999 ◽  
Vol 46 (1) ◽  
pp. 120-134 ◽  
Author(s):  
A.N. Michel
Keyword(s):  
Stability Analysis ◽  
Dynamical Systems ◽  
Hybrid Dynamical Systems ◽  
Recent Trends ◽  
The Stability

A Comparative Study of Liapunov Stability Analyses of Flexible Damped Satellites

1978 ◽  
Vol 45 (3) ◽  
pp. 657-663 ◽  
Author(s):  
H. B. Hablani ◽  
S. K. Shrivastava
Keyword(s):  
Stability Analysis ◽  
Dynamical Systems ◽  
Comparative Study ◽  
Density Function ◽  
Orbital Plane ◽  
Hybrid Dynamical Systems ◽  
Stability Criteria ◽  
Liapunov Stability ◽  
Dynamic Potential ◽  
The Stability

A literal Liapunov stability analysis of a spacecraft with flexible appendages often requires a division of the associated dynamic potential into as many dependent parts as the number of appendages. First part of this paper exposes the stringency in the stability criteria introduced by such a division and shows it to be removable by a “reunion policy.” The policy enjoins the analyst to piece together the sets of criteria for each part. Employing reunion the paper then compares four methods of the Liapunov stability analysis of hybrid dynamical systems illustrated by an inertially coupled, damped, gravity stabilized, elastic spacecraft with four gravity booms having tip masses and a damper rod, all skewed to the orbital plane. The four methods are the method of test density function, assumed modes, and two and one-integral coordinates. Superiority of one-integral coordinate approach is established here. The design plots demonstrate how elastic effects delimit the satellite boom length.

A Survey of Fractional-Order Neural Networks

2017 ◽  
Author(s):  
Shuo Zhang ◽  
YangQuan Chen ◽  
Yongguang Yu
Keyword(s):  
Neural Networks ◽  
Stability Analysis ◽  
Fractional Order ◽  
Computational Science ◽  
General Introduction ◽  
Analysis Methods ◽  
Recent Trends ◽  
The Stability

In this paper, the literature of fractional-order neural networks is categorized and discussed, which includes a general introduction and overview of fractional-order neural networks. Various application areas of fractional-order neural networks have been found or used, and will be surveyed and summarized such as neuroscience, computational science, control and optimization. Recent trends in dynamics of fractional-order neural networks are presented and discussed. The results, especially the stability analysis of fractional-order neural networks, are reviewed and different analysis methods are compared. Furthermore, the challenges and conclusions of fractional-order neural networks are given.

An automated algorithm for stability analysis of hybrid dynamical systems

2013 ◽  
Vol 222 (3-4) ◽  
pp. 757-768 ◽  
Author(s):  
K. Mandal ◽  
C. Chakraborty ◽  
A. Abusorrah ◽  
M. M. Al-Hindawi ◽  
Y. Al-Turki ◽  
...  
Keyword(s):  
Stability Analysis ◽  
Dynamical Systems ◽  
Hybrid Dynamical Systems ◽  
Automated Algorithm

$\mathcal{KL}_*$ -stability for a class of hybrid dynamical systems

2017 ◽  
Vol 82 (5) ◽  
pp. 1043-1060 ◽  
Author(s):  
Bin Liu ◽  
Hai Huyen Heidi Dam ◽  
Kok Lay Teo ◽  
David John Hill
Keyword(s):  
Dynamical Systems ◽  
Dwell Time ◽  
Average Dwell Time ◽  
Hybrid Dynamical Systems ◽  
Uniform Asymptotic Stability ◽  
Time Condition ◽  
Event Time ◽  
Class Function ◽  
The Stability ◽  
Theoretical Results

Abstract This article studies $\mathcal{KL}_*$-stability (the stability expressed by $\mathcal{KL}_*$-class function) for a class of hybrid dynamical systems (HDS). The notions of $\mathcal{KL}_{*}\mathcal{K}_{*}$-property and $\mathcal{KL}_{*}$-stability are proposed for HDS with respect to the hybrid-event-time. The $\mathcal{KL}_{*}$-stability, which is based on $\mathcal{K}$ or $\mathcal{L}$ property of the continuous flow, the discrete jump, and the event in an HDS, extends the $\mathcal{KLL}$-stability and the event-stability reported in the literature for HDS. The relationships between $\mathcal{KL}_{*}\mathcal{K}_{*}$-property and $\mathcal{KL}_{*}$-stability are established via introducing the hybrid dwell-time condition (HDT). The HDT generalizes the average dwell-time condition in the literature. For an HDS with $\mathcal{KL}_{*}\mathcal{K}_{*}$-property consisting of stabilizing $\mathcal{L}$-property and destabilizing $\mathcal{K}$-property, it is shown that there exists a common HDT under which the HDS will achieve $\mathcal{KL}_{*}$-stability. Thus HDT may help to derive some easily tested conditions for HDS to achieve uniform asymptotic stability. Moreover, a criterion of $\mathcal{KL}_{*}$-stability is derived by using the multiple Lyapunov-like functions. Examples are given to illustrate the obtained theoretical results.

Stability of Dynamical Systems With Multiple Nonlinearities

1987 ◽  
Vol 109 (4) ◽  
pp. 410-413 ◽  
Author(s):  
Norio Miyagi ◽  
Hayao Miyagi
Keyword(s):  
Dynamical System ◽  
Stability Analysis ◽  
Dynamical Systems ◽  
Lyapunov Function ◽  
Stability Region ◽  
Direct Method ◽  
Essential Feature ◽  
Point Of View ◽  
Stability Of Dynamical Systems ◽  
The Stability

This note applies the direct method of Lyapunov to stability analysis of a dynamical system with multiple nonlinearities. The essential feature of the Lyapunov function used in this note is a non-Lure´ type Lyapunov function which surpasses the Lure´-type Lyapunov function from the point of view of the stability region guaranteed. A modified version of the multivariable Popov criterion is used to construct non-Lure´ type Lyapunov function, which allow for the dynamical sytems with multiple nonlinearities.

Sign in / Sign up

Export Citation Format

Share Document