WebLocation of Roots Theorem The location of roots theorem is one of the most intutively obvious properties of continuous functions, as it states that if a continuous function attains positive and negative values, it must have a root (i.e. it must pass through 0). Statement Let be a continuous function such that and . Then there is some such that . WebMar 5, 2024 · The root locus plot, as \ (K\) varies from \ (0\) to \ (\infty\), traces a line that proceeds from \ (\sigma =-1\) along the negative real-axis to infinity (Figure 5.1.2). The overlaid grid shows the damping ratio of the closed-loop root (\ (\zeta=1\) in this case).
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