On the application of Liapunov's direct method to discrete dynamic systems with stochastic parameters

Abstract

A Liapunov function specially suitable for the study of the almost sure asymptotic stability of a class of linear discrete systems, described by a set of second order differential equations with stochastic parameters, is presented. A theorem and related corollaries, applicable to systems involving general types of forces, are obtained. The proposed technique is shown to be useful in minimizing the computational efforts associated with relatively large dynamic systems. Several examples, including systems involving follower forces, are included to demonstrate the effectiveness of the method.