Singular Perturbation Theory for Piecewise-Linear Systems with Random Inputs.

摘要

The effect of random inputs on a continuous piecewise-linear singularly perturbed system is investigated in this reprint. Reduced-order models are developed for a second-order system (one fast and one slow variable) which has a random input. It is shown that the solutions of the reduced-order models approximate the actual solution with differences in probability density functions of order O(micron to the one half power) (in a distributional sense). For the special case of a system which is linear in the fast variable, it is shown that the mean-squared error between the approximate and actual solutions in the fast time scale is of order O(micron). An outline is provided for the extension of the results to the vector variable case. Reprints. (kr)