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Lecture 1: System Stability

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Schedule :: Intro :: Signal Models for Discrete-Time :: Signal Operations :: Difference Equations :: Zero-Input :: Zero-State :: Natural & Forced :: System Stability

Plots as a function of pole location. (Asymptotically) stable, unstable, marginally stable.

BIBO stability. System response to bounded inputs:

\begin{displaymath}y[k] = h[k]*f[k]
\end{displaymath}
\begin{eqnarray*}
\vert y[k]\vert &=& \left\vert\sum h[m] f[k-m]\right\vert \\
&\leq& \sum_m \vert h[m]\vert \vert f[m-k]\vert
\end{eqnarray*}

For bounded input, $\vert f[k-m]\vert < K_1 < \infty$
\begin{displaymath}\vert y[k]\vert \leq K_1 \sum_m \vert h[m]\vert
\end{displaymath}
Bounded if $\sum_m \vert h[m]\vert < \infty$ , or all roots inside unit circle.

 

Copyright 2008, by the Contributing Authors. Cite/attribute Resource . admin. (2006, May 16). Lecture 1: System Stability. Retrieved January 07, 2011, from Free Online Course Materials — USU OpenCourseWare Web site: http://ocw.usu.edu/Electrical_and_Computer_Engineering/Signals_and_Systems/1_7node7.html. This work is licensed under a Creative Commons License Creative Commons License