scholarly journals Stability analysis of parabolic linear PDEs with two spatial dimensions using Lyapunov method and SOS

2015 ◽  
Author(s):  
Evgeny Meyer ◽  
Matthew M. Peet
Keyword(s):  
Stability Analysis ◽  
Lyapunov Method ◽  
Spatial Dimensions ◽  
Linear Pdes

THE GRAVITATIONAL ORIGIN OF THE DISTINCTION BETWEEN SPACE AND TIME

2009 ◽  
Vol 18 (14) ◽  
pp. 2155-2158 ◽  
Author(s):  
ASHER YAHALOM
Keyword(s):  
General Relativity ◽  
Stability Analysis ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Flat Space ◽  
Gravitational Theory ◽  
Clear Distinction ◽  
Temporal Dimension ◽  
Spatial Dimensions ◽  
Standard Presentation

To the ordinary human it is obvious that there is a clear distinction between the spatial dimensions, in which one can go either way, and the temporal dimension, in which one seems only to move forward. But the uniqueness of time is also rooted in the standard presentation of general relativity, in which the metric of space–time is locally Lorentzian, i.e. ημν = diag (1, -1, -1, -1). This is presented as an independent axiom of the theory, which cannot be deduced. In this essay I will claim otherwise. I will show that the existence of time should not be enforced on the gravitational theory of general relativity but rather should be deduced from it. The method of choice is linear stability analysis of flat space–times.

Finite-time stability analysis for neutral-type neural networks with hybrid time-varying delays without using Lyapunov method

2017 ◽  
Vol 238 ◽  
pp. 67-75 ◽  
Author(s):  
Mingwen Zheng ◽  
Lixiang Li ◽  
Haipeng Peng ◽  
Jinghua Xiao ◽  
Yixian Yang ◽  
...  
Keyword(s):  
Neural Networks ◽  
Stability Analysis ◽  
Finite Time ◽  
Lyapunov Method ◽  
Neutral Type ◽  
Time Varying ◽  
Time Stability ◽  
Finite Time Stability

scholarly journals Stability Analysis of Nonlinear Systems with Slope Restricted Nonlinearities

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Xian Liu ◽  
Jiajia Du ◽  
Qing Gao
Keyword(s):  
Stability Analysis ◽  
Nonlinear Systems ◽  
Frequency Domain ◽  
Time Domain ◽  
Absolute Stability ◽  
Lyapunov Method ◽  
Lur’E Systems ◽  
Kyp Lemma

The problem of absolute stability of Lur’e systems with sector and slope restricted nonlinearities is revisited. Novel time-domain and frequency-domain criteria are established by using the Lyapunov method and the well-known Kalman-Yakubovich-Popov (KYP) lemma. The criteria strengthen some existing results. Simulations are given to illustrate the efficiency of the results.

A Generalized Mathematical Procedure for Ship Motion Stability Analysis

2009 ◽  
Author(s):  
Ibiba Emmanuel- Douglas
Keyword(s):  
Stability Analysis ◽  
High Performance ◽  
Lyapunov Method ◽  
Analytical Models ◽  
Ship Motions ◽  
Mathematical Framework ◽  
Efficient Design ◽  
Floating Bodies ◽  
Marine Vehicles ◽  
Scientific Disciplines

The challenges of providing safe and high performance marine vehicles present strict and often conflicting constraints that require rational and holistic analysis methodologies to obtain efficient design solutions. This paper presents a mathematical framework for stability analysis, which is one of the key elements in the design and operation of ships and floating bodies that still require considerable improvement. The method is based on the application of the Lyapunov stability analysis concept, which has been highly successful in some other engineering and scientific disciplines. The paper presents the fundamental concepts on the applicability of the Lyapunov method to ship motions stability analysis. Governing mathematical models are derived from first principles and interpreted in the context of geometrical and physical interrelationships. The analytical models are primarily developed for the generalized case of non-linear forced non-conservative systems and simplified by linearization in the case of coupled motion for detailed analysis and characterization of stability conditions and domain. The concept of “motion boundedness” is introduced to satisfy requirements of the Lyapunov method to ship motions subjected to continuous excitations. The analysis leads to some valuable deductions and insight that would be useful in the formulation of stability criteria for ships and marine vehicles in general. The most significant contribution is the possibility of explicit determination of geometric and hydrostatics/hydrodynamics parameters that govern ship stability characteristics.

Stability Analysis of Computer Virus Model System in Networks

2013 ◽  
Vol 278-280 ◽  
pp. 2033-2038 ◽  
Author(s):  
Shao Ting Ge ◽  
Gong You Tang ◽  
Xue Yang ◽  
Qi Lei Xu ◽  
Hao Yu ◽  
...  
Keyword(s):  
Stability Analysis ◽  
Lyapunov Method ◽  
Sufficient Conditions ◽  
Computer Virus ◽  
Model System ◽  
Virus Model ◽  
The Stability ◽  
Conditions Of Stability ◽  
The Mathematical Model ◽  
Disease Free

This paper considers stability analysis of a discrete-time computer virus model in networks. The disease-free equilibrium and the disease equilibrium are first derived from the mathematical model. Then the sufficient condition of stability for the disease-free equilibrium is obtained by the first Lyapunov method. And the sufficient conditions of stability for the disease equilibrium are given by disc theorem. Simulation results demonstrate the effectiveness of the stability conditions.

scholarly journals On Stability of Pin-Jointed Beam Affected by Random Pulsating Load

2017 ◽  
Vol 71 (1-2) ◽  
pp. 63-68
Author(s):  
Jevgeòijs Carkovs ◽  
Andrejs Matvejevs
Keyword(s):  
Mathematical Model ◽  
Stability Analysis ◽  
Lyapunov Method ◽  
Longitudinal Force ◽  
Stability Conditions ◽  
The Stability

Abstract This paper deals with stability analysis of pin-jointed beams that are affected to random pulsating load. The stability conditions of a pin-jointed beam are analysed using a mathematical model of the beam characterised by longitudinal force with Poisson characteristics and applying the stochastic modification of the second Lyapunov method.

Sign in / Sign up

Export Citation Format

Share Document