Multivariate Histograms for Analysis of Linear Control System Robustness

A simple numerical procedure for estimating the stochastic robustness of a linear, time-invariant system is described. Based on Monte Carlo evaluation of the system´s eigenvalues, this analysis approach introduces the probability of instability as a scalar measure of stability robustness. The related stochastic root locus, a portrayal of the root probability density, provides insight into robustness characteristics. Parameter uncertainties are not limited to Gaussian distributions; non-Gaussian cases, including uncertain-but-bounded variations, can be considered as well. Confidence intervals for the scalar probability of instability address computational issues inherent in Monte Carlo simulation. An example demonstrates stochastic robustness as applied to a physical system with Gaussian, uniformly distributed, and binary parameters.