A Test for Time-Dependence of Linear Open-Loop Systems

Summary We consider the problem of testing a given open-loop system for time-dependence. The test is based on just a single realization of the input and a single realization of the output. It makes use of the concept of the “evolutionary cross-spectra” of a non-stationary vector process and rests essentially on testing the “uniformity” of a set of vectors, whose components consist of the “evolutionary gain-spectra” and “evolutionary phase-spectra”. Using a logarithmic transformation on the evolutionary gain-spectra, we show that the mechanics of the test are formally equivalent to a two-factor multivariate analysis of variance (MANOVA) procedure. Numerical illustrations of the proposed test procedure are included.