Stability

Stability

1. Types stability

   • Stable
     • entrance bounded / bounded output
     • stable zero input (When t approaches infinity)
     • The poles of its transfer function is in the left half plane
   • Marginally stable
     • If there are no roots of the characteristic polynomial in the right half plane
     • If no roots on the imaginary axis
   • Unstable
     • If there are roots of the characteristic polynomial in the right half plane
     • If a coefficient foul on the characteristic equation or negative

2. Degrees of stability

   • Absolute stability
     • The system is stable (Polo negative real part) or unstable (Polo positive real part)
   • Relative stability
     • Determining quantitatively how stable a system
       • Evaluate how close / far this contour transformed be unstable

3. Tools for stability analysis

   • Nyquist criterion
   • Bode plot
   • Nichols plot
   • Routh criterion

4. In the stability study only the poles of the transfer function are important

   • characteristic polynomial.
   • He concept Stability is applied to closed loop systems or open loop

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