Stability Analysis of Uncertain Systems Using a Singular Value Decomposition-Based Metric

Abstract

The stability of dynamic systems is important for satisfactory performance, safety and reliability. The study becomes more difficult when the system is nonlinear and when the ever present uncertainties in the components are considered. Herein a new approach is presented that uses time-domain information: It invokes design of experiments based on the uncertainty within the system, computer simulation of the dynamics to generate a matrix of discrete time responses that presents the variability of the response, and finally, singular value decomposition to separate out parameter information from time information. The variability in the elements in the first few left singular vectors predicts any instability that might occur over the complete life-time of the system. The key to the approach is the introduction of random variables and subsequent co-variance operations. A real-world example and comparison to established methods show the efficacy of the approach.