The Stability of a System with Periodically Varying Parameters

This paper deals with the stability of a second-order linear system whose dynamic behavior is governed by
\ddot{x}(t) + a(t)\dot{x}(t) + b(t)x(t) = 0
where
a(t)
and
b(t)
are periodic functions which vary in rectangular form with respect to the time
t
. A generalized stability condition is derived and stability charts are shown as the relationship between system parameters. These stability charts are obtained by using a digital computer. A more precise stability chart is shown for
a(t) = 0
than those given hitherto in other reports.