On the Almost Sure Stability of Linear Stochastic Systems

1970 ◽  
Vol 37 (2) ◽  
pp. 541-543 ◽  
Author(s):  
F. T. Man
Keyword(s):  
Asymptotic Stability ◽  
Stochastic Systems ◽  
Sufficient Condition ◽  
Almost Sure Stability ◽  
Linear Stochastic Systems ◽  
Region Of Stability

A new sufficient condition for the almost surely asymptotic stability of ergodic coefficient linear stochastic systems is presented and is compared with previously published results. Two examples are given to illustrate the sufficient condition thus derived and to demonstrate the considerable extension, using this method, of the region of stability over the existing results.

On the Almost Sure Stability of Linear Stochastic Systems

1978 ◽  
Vol 34 (4) ◽  
pp. 643-656 ◽  
Author(s):  
A. Parthasarathy ◽  
R. M. Evan-Iwanowski
Keyword(s):  
Stochastic Systems ◽  
Almost Sure Stability ◽  
Linear Stochastic Systems

Almost-Sure Stability of Some Linear Stochastic Systems

1989 ◽  
Vol 56 (1) ◽  
pp. 175-178 ◽  
Author(s):  
S. T. Ariaratnam ◽  
B. L. Ly
Keyword(s):  
Stochastic Systems ◽  
Stability Boundary ◽  
Quadratic Function ◽  
Random Processes ◽  
Almost Sure Stability ◽  
Special Cases ◽  
Linear Stochastic Systems ◽  
The Matrix ◽  
The Stability ◽  
Second Order Systems

The almost-sure stability of linear second-order systems which are parametrically excited by ergodic, “nonwhite,” random processes is studied by an extension of the method of Infante. In this approach, a positive-definite quadratic function of the form V = x′Px is assumed and a family of stability boundaries depending on the elements of the matrix P is obtained. An envelope of these boundaries is then solved for by optimizing the stability boundary with respect to the elements of P. It is found that the optimum matrix P in general depends not only on the system constants but also on the excitation intensities. This approach is, in principle, applicable to study systems involving two or more random processes. The results reported in previous investigations are obtained as special cases of the present study.

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.

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