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Lecture #09

This lecture covers stability analysis of LTI systems using S-domain analysis. Topics include absolute stability, Routh-Hurwitz criteria, relative stability, steady-state error, root locus, and Bode plot. The lecture also discusses testing for stability using properties of polynomial coefficients.

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Lecture #09

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  1. Lecture #09 LTI system stability S-domain analysis signals & systems

  2. Stability analysis • Absolute Stability • Routh-Huwitz criteria • Relative Stability • Steady state error • Root locus • Bode plot signals & systems

  3. Stability testing • Properties of the polynomial coefficients : • Differing algebraic signs • Zero-valued coefficients • All of the same algebraic sign, non zero At least one RHP root Has imaginary axis roots or RHP roots or both No direct information signals & systems

  4. Routh-Hurwitz testing The number of RHP roots of P(s) isthe number of algebra sign changes in the elements of the left column of the array. signals & systems

  5. Example 1 Two roots in the RHP signals & systems

  6. Example 2 no root in the RHP signals & systems

  7. Example 3 n 移位次數移至0消失為止 Two roots in the RHP signals & systems

  8. Example 4 factor signals & systems

  9. no root in the RHP signals & systems

  10. + - Example 5 signals & systems

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