Almost-Sure Stability of Some Linear Stochastic Systems

[+] Author and Article Information
S. T. Ariaratnam

Solid Mechanics Division, University of Waterloo, Waterloo, Ontario, Canada, N2L 3G1

B. L. Ly

Civil Engineering Branch, Atomic Energy of Canada Limited, Mississauga, Ontario, Canada, L5K 1B2

J. Appl. Mech 56(1), 175-178 (Mar 01, 1989) (4 pages) doi:10.1115/1.3176041 History: Received October 29, 1987; Revised June 24, 1988; Online July 21, 2009


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.

Copyright © 1989 by ASME
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