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Similarity Transformation

Similarity Transformation. Basic Sets. Use a new basis set for state space. Obtain the state-space matrices for the new basis set. Similarity transformation. Transformation. Realization. Transformation to Diagonal Form. Example 7.18. Solution. Companion Form. Diagonal Form.

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Similarity Transformation

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  1. Similarity Transformation

  2. Basic Sets • Use a new basis set for state space. • Obtain the state-space matrices for the new basis set. • Similarity transformation.

  3. Transformation

  4. Realization

  5. Transformation to Diagonal Form

  6. Example 7.18

  7. Solution

  8. Companion Form

  9. Diagonal Form

  10. Invariance of TF & Characteristics equation Theorem 7.1: Similar systems have identical transfer functions and characteristic polynomial.

  11. Proof

  12. Equivalent Systems Systems with the same transfer function Example 7.20 Show that the following system is equivalent to the system of 7.17(2). x(k + 1) =0 8187 x(k) + 9 0635 × 10−2 u(k) y(k) = x(k) Solution: The transfer function of the system is G(z) = 9.0635 × 10−2/(z− 0.8187) Identical to the reduced transfer function of Example 7.17(2).

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