Question

Determine whether the following systems are BIBO-Stable or non-BIBO-Stable

A)y(t)=x²t
B) y(t)=∫[infinity]t x(r)dr

Answer 1

A system is BIBO stable if the output remains bounded for all bounded inputs. System A is non-BIBO stable, while system B is BIBO stable.

Step-by-step explanation:

A system is said to be BIBO (Bounded Input Bounded Output) stable if the output remains bounded for all bounded inputs. To determine if a system is BIBO stable, we need to analyze the behavior of the output for different inputs. Let's analyze the given systems:

a) In the system y(t) = x^2t, the input is x(t) = t, and the output is y(t) = x^2t = t^3. Since the output increases as the input increases, this system is non-BIBO stable.

b) In the system y(t) = ∫[∞t] x(r)dr, the input is x(t) and the output is the integral of x(t) over the time interval [t,∞]. Since the integral represents the area under the curve of x(t), which can be bounded for bounded inputs, this system is BIBO stable.