Stability

Stability

1. TYPES OF STABILITY

   • Stable
     • BIBO: bounded input, bounded output
     • Stable zero input (t->infinity)
     • poles of transfer function in the left-half plane
   • Marginally Stable
     • No roots of the characteristic polynomial in the right-half plane
     • No roots on the imaginary axis
   • Unstable
     • Roots in the right-half plane
     • if missing coefficients or there are a negative one

2. The utmost important requirement in control system design is the stability.

3. Degrees of Stability

   • Absolute Stability
     • Only takes into consideration the position of the poles with respect to the plane
   • Relative Stability
     • Determines how stable the system is

4. It is ANALYZED trough

   • Routh Criterion
   • Nyquist Criterion
   • Bode plot
   • Nichols plot

5. Only the poles are important for their analysis

   • characteristic polynomial.
   • applied to close and open loop systems

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