Question

Discuss asymptotic and BIBO stabilities for the systems described by the following trans fer functions, assuming that the systems are controllable and observable:

(s + 5) / s² +3s +2

Answer 1

The system described by the transfer function is both asymptotically stable and BIBO stable.

Step-by-step explanation:

To determine the asymptotic and BIBO stabilities of a system described by the transfer function (s + 5) / (s² + 3s + 2), we need to analyze the poles of the transfer function. The poles are the values of 's' that make the denominator of the transfer function zero. In this case, the denominator is s² + 3s + 2, which can be factored as (s + 1)(s + 2). So, the poles of the transfer function are at s = -1 and s = -2.

For asymptotic stability, all the poles of the transfer function must have negative real parts. In this case, both poles have negative real parts (-1 and -2), so the system is asymptotically stable.

For BIBO (Bounded-Input Bounded-Output) stability, the transfer function must have a finite upper limit on the output for any bounded input. Since the poles of the transfer function have negative real parts, the system is BIBO stable.