Abstract
Many studies have shown that arbitrarily small differences between two nonconservative dynamic systems can result in completely different stability characteristics of the two systems. This can be interpreted as implying that mathematical modeling is of questionable value in the analysis and design of physical nonconservative systems. Using basic results from Liapunov stability theory, two rules for avoiding such infinite-sensitivity models are proposed for the mathematical modeling of discrete dynamic systems. Several general types of modeling error are considered, and these rules are shown to assure finite-sensitivity models.
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