Stochastic Sample Stability of Oscillatory Systems

1988 ◽  
Vol 55 (2) ◽  
pp. 458-460 ◽  
Author(s):  
S. T. Ariaratnam ◽  
W.-C. Xie
Keyword(s):  
Asymptotic Stability ◽  
Stability Condition ◽  
Gaussian Noise ◽  
Damping Coefficient ◽  
Sufficient Condition ◽  
Order Linear ◽  
Oscillatory Systems ◽  
Sample Stability ◽  
Probabilistic Property ◽  
Asymptotic Stability Condition

A method of obtaining a sufficient almost-sure asymptotic stability condition for second-order, linear oscillatory systems with an ergodic damping coefficient is presented. In this method, the probabilistic property of the derivative process of the damping coefficient is taken into account. A sufficient condition for almost-sure asymptotic stability is derived and numerical results are presented for the case of a Gaussian noise coefficient. The results are found to be an improvement over previously available results for oscillatory systems with stochastic damping.

Effect of Correlation on the Almost-Sure Asymptotic Stability of Second-Order Linear Stochastic Systems

1989 ◽  
Vol 56 (3) ◽  
pp. 685-690 ◽  
Author(s):  
S. T. Ariaratnam ◽  
Wei Chau Xie
Keyword(s):  
Asymptotic Stability ◽  
Gaussian Noise ◽  
Stochastic Systems ◽  
Second Order ◽  
Order Linear ◽  
Stiffness Coefficients ◽  
Special Cases ◽  
Linear Stochastic Systems ◽  
Probabilistic Property ◽  
Asymptotic Stability Condition

A method of obtaining a sufficient almost-sure (a.s.) asymptotic stability condition for second-order, linear systems with both ergodic damping and stiffness coefficients is presented. The probabilistic property of the correlation between the damping and stiffness coefficients is taken into account. A sufficient condition for a.s. asymptotic stability is derived and numerical results are presented for the case of Gaussian noise coefficients. Results obtained in some of the previous investigations are included in the present study as special cases.

scholarly journals An asymptotic stability condition for inhomogeneous simple shear

1989 ◽  
Vol 47 (2) ◽  
pp. 247-262 ◽  
Author(s):  
H. Tz. Chen ◽  
A. S. Douglas ◽  
R. Malek-Madani
Keyword(s):  
Asymptotic Stability ◽  
Simple Shear ◽  
Stability Condition ◽  
Asymptotic Stability Condition

DELAY-DEPENDENT ASYMPTOTIC STABILITY OF NEURAL NETWORKS WITH TIME-VARYING DELAYS

2008 ◽  
Vol 18 (01) ◽  
pp. 245-250 ◽  
Author(s):  
SHENGYUAN XU ◽  
JAMES LAM ◽  
DANIEL W. C. HO
Keyword(s):  
Neural Networks ◽  
Stability Analysis ◽  
Asymptotic Stability ◽  
Stability Condition ◽  
Linear Matrix ◽  
Time Varying ◽  
Matrix Inequality ◽  
Unique Equilibrium ◽  
Delay Dependent ◽  
Asymptotic Stability Condition

This paper considers the problem of stability analysis for neural networks with time-varying delays. The time-varying delays under consideration are assumed to be bounded but not necessarily differentiable. In terms of a linear matrix inequality, a delay-dependent asymptotic stability condition is developed, which ensures the existence of a unique equilibrium point and its global asymptotic stability. The proposed stability condition is easy to check and less conservative. An example is provided to show the effectiveness of the proposed condition.

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