Continuous Time

Info

Continuous means to extend without interruption

Controls Applications

Physical plants are always CT systems since the output signal needs to exist in continuous time.

• Sampled Data Digital Control Systems

Stability

• See Stability

1. $\mathrm{Re}\left(\lambda \right)<0$
   • Decays over time with oscillations
   • Stable
2. $\mathrm{Re}\left(\lambda \right)>0$
   • Grows exponentially with oscillations
   • Unstable

• $\mathrm{Re}\left(\lambda \right)=0$
  • Oscillations about an axis
  • This used to be called marginally stable, but is unstable because it never returns to 0

$e^{\lambda t}=e^{\mathrm{Re}\lambda t}+e^{j\mathrm{Im}\lambda t}$ where the real component controls growth or decay, and the imaginary component controls oscillations