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Using the bilinear transformation and rouths stability

Consider the forward loop transfer function in the sampled-data system with a zero-order hold in cascade as:

G_c(z) · G(z) = K(z + 1) / (z - 1) (z - 0.2)²

Using the bilinear transformation and Routh's Stability Criterion find the range of value of the gain for the system remains stable.

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Algebra: Using the bilinear transformation and rouths stability

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Algebra: Using the bilinear transformation and rouths stability

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