A linear system is said to be stable if its impulse

Chapter 7, Problem 31E

(choose chapter or problem)

A linear system is said to be stable if its impulse response function \(h(t)\)

 remains bounded a \(t \rightarrow+\infty\). If the linear system is governed by

\(a v^{\prime \prime}+b v^{\prime}+c v=g(t)\) where \(b\) and \(c\) are not both zero, show that the system is stable if and only if the real parts of the roots to \(a r^{2}+b r+c=0\) are less than or equal to zero.

Equation Transcription:

 

Text Transcription:

h(t)

 T right arrow + infinity

ay''+by'+cy=g(t)

b

c

ar^2+br+c=0