The Influence of System Stability and Dynamics on the Accuracy of Level-Crossing Prediction

This technical note investigates the effect of stability on the probability of correctly predicting level-crossings for the output of a linear dynamical system driven by Gaussian noise. It is found that decreasing the stability margin has a favorable effect on predictive capability. The insight from this finding was derived from a parametric analysis of a given measure of predictive capability, represented as an explicit function of the spectral radius. The formulae used to characterize this relationship were derived under strict technical conditions in previous work. However, as a result of the closed-form nature of these expressions, using these formulae to gain insight on the influence of stability was much more computationally efficient than would otherwise be possible under more relaxed technical conditions.