On the Use of Empirical Gramians for Controllability and Observability Analysis

This short paper illustrates the use of empirical gramians for controllability/observability analysis of nonlinear systems and compares the extracted information to results obtained from linear gramians and nonlinear observability matrices. It is shown that empirical gramians can more accurately represent controllability/observability of a nonlinear system over an operating region than if linear gramians are used. At the same time the information contained in empirical gramians is easier to extract and interpret than if Lie algebra-based controllability or observability matrices are used.